WALSH 
BUSINESS 
RITHMETIC 


JOHN  HENRY  WALSH 


GIFT   OF 


WALSH'S 
BUSINESS   ARITHMETIC 


BY 

JOHN  H.   VSfALSH 

ASSOCIATE  SUPERINTENDENT  OF  SCHOOLS,    THE  CITY  OF  NEW  YORK 


THE    GREGG    PUBLISHING    COMPANY 

NEW  YORK  BOSTON  CHICAGO  SAN  FRANCISCO 

ENGLAND:  21  HARRINGTON  STREET,  LIVERPOOL 


.^ 


COPYRIGHT,    IQIQ,    BY  THE 
GREGG    PUBLISHING    COMPANY 


PREFACE 

IN  this  work  the  author  has  kept  in  mind  the  needs 
of  boys  and  girls  that  have  taken  up  a  commercial 
course.  The  latter  generally  requires  the  completion 
of  the  arithmetical  portion  by  the  end  of  the  first  year 
of  high  school,  and  care  has  been  taken  to  keep  the 
problems  within  the  capacity  of  pupils  at  this  stage. 

Section  I,  Recording  Business  Transactions,  presents 
briefly  the  clerical  tasks  likely  to  confront  boys  and 
girls  upon  their  entrance  into  the  business  world;  the 
calculations  they  are  expected  to  make,  the  simple 
accounts  they  may  be  required  to  keep,  the  commoner 
"forms"  they  will  use,  etc. 

In  Section  II,  Business  Calculations,  are  given  com- 
putations in  percentage,  trade  discount,  interest,  and 
bank  discount,  made  in  the  ways  employed  by  business 
men. 

The  arrangement  that  assigns  Numbers  and  Pro- 
cesses to  Section  III  does  not  mean  that  practice  in 
these  topics  should  be  deferred  until  pupils  have  com- 
pleted the  two  previous  sections.  It  is  expected  that 
the  teacher  will  take  from  this  portion  of  the  book  oral 
exercises  for  short  daily  drills,  and  abstract  written 
ones  weekly,  for  a  longer  period,  to  give  facility  and 
accuracy. 

In  this  section  the  pupil  is  shown  the  business  way  of 
reading  numbers,  some  short  cuts  used  in  the  several 


5I> 


iv  PREFACE 

processes,  methods  of  combining  two  operations,  and 
the  manner  in  which  results  should  be  tested. 

In  the  remaining  four  sections  are  presented  the 
arithmetical  treatment  of  conditions  arising  in  the 
various  departments  of  business,  taken  in  the  order  of 
their  importance  and  of  their  availability  for  the  in- 
struction of  the  young  student.  Every  boy  and  every 
girl,  regardless  of  his  or  her  subsequent  career,  will  be 
benefited  by  the  work  done  in  Problems  of  the  Con- 
sumer, Chapter  One  of  Section  IV.  In  Chapter  Two 
of  this  section,  Problems  of  the  Producer,  those  of  the 
farmer  have  been  chosen  as  typical.  Later  on,  the 
baker  is  made  the  typical  manufacturer.  Broad 
treatment  of  conditions  readily  understandable  has 
been  the  aim. 

It  is  not  expected  that  all  of  the  work  here  presented 
will  be  completed  in  a  year.  The  teacher  should  make 
intelligent  selections  from  the  material  offered. 


CONTENTS 

SECTION  I 

RECORDING  BUSINESS  TRANSACTIONS 
CHAPTER  ONE.  — LEARNING  BY  DOING 

PAGE  PAGE 

A  Boy's  Cash  Book 1       The  Record  Strip 11 

Single-entry  Ledger 3       The  Bookkeeper 13 

A  Better  Way 6       The  Bank  Account 18 

CHAPTER  Two.  —  A  GIRL  IN  BUSINESS 

Sales  Girl    .  24       The  Time  Clock 36 

Bill  Clerk 28       Time  Sheet 38 

Office  Assistant 31       Wage  Tables 41 

CHAPTER  THREE.  — SOME  BUSINESS  FORMS 

Invoices  and  Bills 44       Orders  for  Goods 52 

Bill  for  Services,  etc 49       Bill  of  Lading 54 

Receipts      50       Freight  Bill 55 

SECTION  II 

BUSINESS   CALCULATIONS 
CHAPTER  ONE.  —  PERCENTAGE 

Finding  the  Percentage    ...       58       Finding  the  Base 69 

Aliquot-part  Method    ....       62       Rate  of  Profit 74 

Finding  the  Rate 63       Net  Profit 76 

CHAPTER  Two.  — COMMERCIAL  DISCOUNT 

Cash  Discount 77       Compound  Discounts  ....       80 

List  Prices      78      Quantity  Discounts 87 

CHAPTER  THREE.  — SIMPLE  INTEREST 

Lending  Money 89       Aliquot-part  Method    ....       96 

Promissory  Notes 90       Sixty-day  Method 102 

Cancellation  Method    .  94       Six  Per  Cent  Method   .  107 


vi  CONTENTS 


CHAPTER  FOUR.  — BANK  DISCOUNT 

Discounting  the  Note  ....     110      Term  of  Discount 116 

Date  of  Maturity      114      Interest-bearing  Note  ....     120 


SECTION  III 

NUMBERS  AND  PROCESSES 

CHAPTER  ONE.  — READING  AND  WRITING  NUMBERS 

Reading  Decimals 126  Roman  Numbers 133 

The  Business  Way 127  Graphs 187 

Dictating  Dollars  and  Cents  .  129  Reading  Meters 142 

Writing  Per  Cents 132  Marking  Goods 145 

CHAPTER  Two.  —  PROPERTIES  OF  NUMBERS 

Composite  Numbers     ....     149       Least  Common  Multiple     .    .     151 
Prime  Numbers 149      Divisibility  of  Numbers  .    .    .     152 

CHAPTER  THREE.  —  REDUCTIONS 

Reducing  Fractions 155  Denominate  Numbers  ....  159 

Simplifying  Complex  Fractions  157  Reducing  Fractions 166 

Changing  Decimals   to  Com-  Reducing  Decimals 175 

mon  Fractions 159 

CHAPTER  FOUR.  — SIGNS  AND  OPERATIONS 

Arithmetical  Signs 183       Signs  of  Aggregations  ....     185 

Precedence  of  Signs 184       Indicating  Operations  ....     186 

CHAPTER  FIVE.  —  ADDITION 

Counting  Exercises 190       Adding  Fractions 200 

Adding  Integers  and  Decimals     194       Adding  Compound  Numbers  .     208 

CHAPTER  Six.  —  SUBTRACTION 

Making  Change 210  Subtracting  Compound  Num- 

Subtracting  Integers     ....  211  bers 226 

Adding  and  Suhtnicting  .    .    .  214  Time  between  Dates    ....     228 

Subtracting  Fractions  ....  222 

CHAPTER  SEVEN.  —  SPECIAL  TESTS 

Avoiding  Mistakes 232      Casting  out  9*s 234 

Testing  Resulta 232      Casting  out  ll's 237 


CONTENTS  vii 

CHAPTER  EIGHT.  —  MULTIPLICATION 

Multiplying  and  Adding  .    .    .     244       Multiplying  Decimals  ....     275 

Using  Factors 251       Multiplying  Denominate  Num- 

Multiplying  Fractions  ....     260          bers 278 

Aliquot  Parts 265 

CHAPTER  NINE.  —  DIVISION 

Dividing  by  an  Integer    .    .    .  279  Dividing  by  Factors     ....  291 

Short  Division 281  Dividing  by  Multiples      ...  293 

Decimal  Quotients 285  Decimal  Divisors 300 

Decimal  Dividends 286  Abbreviated  Division  ....  307 

Denominate  Dividends    .    .    .  288  Cancellation 311 

Fractional  Dividends    ....  289  Division  of  Fractions    ....  313 

SECTION  IV 

PRODUCTION  AND  CONSUMPTION 

CHAPTER  ONE.  —  PROBLEMS  OF  THE  CONSUMER 

Family  Budgets 318       Household  Account 336 

''Balanced"  Meals 324       Inventory 340 

Efficiency  in  Home  Keeping     .     328       Insurance 342 

CHAPTER  Two.  —  PROBLEMS  OF  THE  PRODUCER 

Farming  as  a  Business     .    .    .     343       Milk  Production 347 

Receipts  and  Expenses    .    .    .     346      Cost  of  a  Crop 349 

SECTION  V 

FROM  THE  PRODUCER  TO  THE  CONSUMER 

CHAPTER  ONE.  —  BUYING  AND  SELLING  AGENCIES 

Commission 357       Selling  Through  a  Broker  .    .     361 

The  Local  Buyer 359       Storage 365 

CHAPTER  Two.  — TRANSPORTATION  PROBLEMS 

Animal  Transportation    .    .    .  368  Express 373 

Improved  Roads 370  The  Mail  Matter 375 

Railroad  Transportation      .    .  370  Rates  of  Postage 375 

Water  Transportation  ....  372  Parcel  Post 377 

CHAPTER  THREE.  —  PROBLEMS  OF  THE  MANUFACTURER 

Making  and  Selling  Bread  .    .     378       Profit  and  Loss      386 

Factory  Costs 383       Overhead  Expenses 387 

CHAPTER  FOUR.  —  THE  MERCHANT'S  PROBLEMS 

The  Retail  Butcher 389       Depreciation 394 

Daily  Shoe  Sales 390      A  Wholesale  Business  ....     396 


viii  CONTENTS 

CHAPTER  FIVE.  —  PARTNERSHIP 

Partnership  Agreements  ...     397      Division  of  Profits 398 

SECTION  VI 

FINANCING  BUSINESS 

CHAPTER  ONE.  — REMITTING  MONEY 

Money  Orders 401       Trade  Acceptances 409 

Telegraphic  Transfers  ....     402       Bills  of  Exchange 413 

Bank  Drafts 404       Documentary  Bills 414 

CHAPTER  Two.  —  BANKS  AND  BANKING 

Banks  of  Deposit  and  Discount    417       Certificate  of  Deposit  ....     426 

Collateral  Loans 418       Interest  on  Balances     ....     427 

Accurate  Interest 424       Savings  Accounts 428 

CHAPTER  THREE.  — STOCKS  AND  BONDS 

Forming  a  Corporation    ...     431       Bonds      438 

Par  Value  of  Stock 432       Accrued  Interest 440 

Stock  Prices 433       Rate  of  Income 442 

CHAPTER  FOUR.  — FINANCING  THE  GOVERNMENT 

The  Taxpayer 443       United  States  Revenues  ...     41!) 

The  Budget 443       Duties 450 

State  Revenues 443      The  Tariff l.io 

CHAPTER  FIVE.  — PROTECTING  THE  INDIVIDUAL 
Fire  Insurance  .  454      Short-term  Rates  .  456 


SECTION  VII 

BUSINESS  MEASUREMENTS 

CHAPTER  ONE.  — COMMON  TABLES 

Weights  and  Measures     .    .    .     458       Square  Measure 465 

Metric  System 461       Cubic  Measure 466 

(MM-TER  Two.  — AREAS  AND  VOLUMES 

Lines  and  Angles 4(W  Hoard  Mc.isim- 484 

Area  of  Rectangle 470  The  Cirrlr isi; 

Triangles 475  Prism  and  Cylinder 491 

Powers  and  Roots 476  Pyramid  ami  Cone 493 


WALSH'S 
BUSINESS    AEITHMETIC 

SECTION  I 

RECORDING  BUSINESS  TRANSACTIONS 

CHAPTER  ONE 
LEARNING  BY  DOING 

While  Edward  Kerr  was  still  attending  school  he 
obtained  employment  during  his  spare  time  in  Hiram 
Hunt's  general  store. 

Being  very  methodical,  Edward  kept  an  account 
of  his  receipts  and  expenditures  in  a  pocket  memo- 
randum book,  in  the  following  form: 

A  PAGE   OF  A  BOY'S   CASH  BOOK 


1919 

•    Sep.* 

1 

« 

« 

2 
3 
6 

7 
8 

On  hand 
Penknife 
War  Savings  Stamps 
Moving  Pictures 
Tie 
Wages 
Hair  cut 
Church 
Balance 

On  hand 
School  supplies 
Car  fare 
Lunch 
Athletic  dues 

15 
3 

74 
50 

10 
7 

75 

10 
30 

25 
25 
59 

24 

45 
10 
20 
25 

19 

24 

19 

« 

8 

M 

7 

59 

4 

The  abbreviations  for  the  names  of  the  months  are  those  used  by  business  houses. 

1 


2    •  :  ,\VAl£H'S.  Bfi&NESS   ARITHMETIC 

The  first  entry  on  this  page  shows  the  cash  on  hand,  the 
amount  being  written  in  the  first  double  money  column. 
The  next  four  items  are  expenditures,  the  amount  of  each 
being  placed  in  the  second  money  column.  Then  follow 
a  cash  receipt  and  two  expenditures.  In  writing  each  debit 
item  Edward  began  close  to  the  date  column,  and  began 
each  credit  item  one-half  inch  to  the  right. 

BALANCING  THE  ACCOUNT 

He  closed  the  account  at  the  end  of  the  week  by 
writing  the  word  "Balance"  in  red  ink  as  the  last 
item.  He  then  drew  a  line  across  the  money  columns, 
and  below  it  wrote  19.24,  the  total  of  the  debits,  in 
the  debit  (Dr.)  money  column,  and  the  same  amount 
in  the  credit  (Cr.)  column.  He  inserted  the  balance, 
7.59,  in  red  ink  in  the  Cr.  column.  This  balance  he 
obtained  as  follows: 

Adding  downward,  he  thought  — 10  (5  +  5),  15  (adding 
5)  and  9  (writing  9)  are  24; 

•  9  (carrying  2),  10  (adding  1),  13  (adding  3),  15  (adding 
2),  17  (adding  2),  and  6  (writing  5),  are  22; 

12  (carrying  2),  and  7  (writing  7),  are  19. 

He  tested  the  correctness  of  the  balance  by  covering  the 
second  total,  19.24,  with  a  strip  of  paper,  on  which  he  wrote 
the  total  obtained  by  adding  the  second  column  upward. 

He  then  counted  his  cash  on  hand,  and  finding  that  it 
amounted  to  7.59,  he  frit  sure  that  he  had  entered  all  of 
the  cash  transactions  for  the  week. 

He  next  drew  a  double  line  below  the  totals  and  also 
across  the  date  column,  and  on  the  line  below  he  reopened 
tin-  account  by  the  entry  "Sep.  8,  On  hand,  7.59." 

If  he  desired  to  ascertain  his  available  cash,  he  would 
add  7.59  to  the  balance  shown  by  his  savings-bank  book, 
his  War  Savings  Stamps,  etc. 


RECORDING   BUSINESS   TRANSACTIONS 


WRITTEN  EXERCISE 

Copy  the  foregoing  account,  and  supply  additional 
items  to  cover  the  transactions  of  the  remainder  of 
the  second  week.  Close  the  account  on  the  morning 
of  September  15,  by  inserting  the  balance,  and  re- 
open it  the  same  day. 

Use  a  sheet  of  journal  paper,  or  one  ruled  in  the  form  shown  in 
the  foregoing  account.  On  the  top  line  write  the  word  "Cash,"  but  omit 
the  abbreviations  "Dr."  and  "Cr."  Do  not  use  the  dollar  sign  ($). 

PAGE   OF  A   SINGLE-ENTRY  LEDGER 

Mr.  Hunt's  bookkeeping  was  limited  to  the  accounts 
he  kept  with  the  few  customers  to  whom  he  extended 
credit.  To  each  of  these  he  assigned  a  page  in  a 
ledger.  He  kept  this  book  by  single  entry;  that  is, 
he  entered  each  transaction  but  once. 

The  following  shows  the  account  of  John  McKeon,  which 
was  kept  on  page  15 : 


JOHN  McKEON 


Dr.          Cr. 


1920 

May 

1 

25  Ib.  Sugar        .08                    2.— 

5  "  Tea           .35                     1.75 

20yd.  Muslin    .12                    2.40 

1  bbl.  Flour                                9.50 

15 

65 

6 

8doz.  Eggs       .35                    2.80 

Cash                                          10.— 

12 

80 

9 

10  Ib.  Coffee       .29 

2 

90 

27 

Cash  in  full 

5 

75 

18 

55 

18 

55 

The  foregoing  shows  that  Mr.  McKeon  on  May  1,  1920, 
received   goods   to   the  amount    of   $15.65,   for    which   he 


4  WALSH'S   BUSINESS    ARITHMETIC 

did  not  pay  at  the  time;  and  that  on  May  9  he  similarly 
received  goods  to  the  amount  of  $2.90.  It  shows  that  on 
May  6  he  paid  a  total  of  $12.80  in  cash  and  produce,  and 
that  on  May  27  he  settled  in  full  by  a  cash  payment  of 
$5.75. 

Only  the  footing  of  a  day's  purchases  was  carried  to  the 
money  columns,  the  separate  extensions  being  written  in 
the  space  to  the  left. 

The  first  double  money  column  (Dr.)  shows  the  debits 
of  John  McKeon  to  the  store,  the  second  shows  the  credits 
due  by  the  store  to  him. 

When  Mr.  McKeon  called  on  May  27  to  pay  the  balance 
he  owed,  this  was  determined  by  deducting  his  credits  of 
$12.80  from  $18.55,  the  sum  of  his  debits.  This  difference, 
$5.75,  was  then  paid,  and  entered  as  a  credit. 

In  the  foregoing  account,  the  items  2. — ,  1.75,  2.40,  9.50, 
etc.,  are  called  extensions.  The  total,  15.65,  is  called  a 
footing. 

WRITTEN  EXERCISE 

Make  out  an  account  similar  to  the  foregoing.  Use 
prices  prevailing  in  the  vicinity  of  the  school.  Make 
the  total  of  the  Dr.  money  column  agree  with  that  of 
the  Cr.  column  by  the  insertion  of  the  necessary 
amount.  Draw  a  line  across  the  page  to  show  that 
the  account  is  closed. 

NOTE:  Omit  unnecessary  words,  figures,  etc.  Do  not  write  Dr.  and 
Cr.  above  their  respective  columns.  Omit  the  dollar  sign  ($). 

ANTIQUATED   METHODS 

Mr.  Hunt  made  no  entries  of  lii^  tr.-msadtions  with  the 
merchants  from  whom  he  purchased  goods.  When  he 
bought  on  credit,  he  placed  the  bill  in  a  tray  until  it  be- 
came due,  and  when  it  was  receipted,  he  filed  it  away  with 
other  receipted  bills. 


RECORDING    BUSINESS    TRANSACTIONS  5 

He  kept  no  cash  account.  At  the  close  of  business  each 
day,  he  counted  the  money  in  the  drawer,  deducted  from 
the  total  the  amount  placed  in  the  drawer  in  the  morning 
to  be  used  in  making  change,  and  added  to  the  balance 
the  total  of  the  cash  payments  taken  from  the  drawer. 
If  the  final  result  agreed  with  the  total  cash  sales  for  the 
day,  as  shown  on  the  strip  in  the  cash  register,  he  was 
satisfied. 

Not  having  had  experience  with  anything  different, 
Mr.  Hunt  felt  only  vaguely  the  advantages  of  a  system 
that  would  enable  him  to  ascertain  his  business  condition 
at  any  time,  the  expense  of  selling  goods,  and  the  like. 

CHARGING  THE  WRONG  ACCOUNT 

It  happened  once  in  a  while  that  in  the  hurry  of  busi- 
ness the  account  of  one  customer  was  debited  with  goods 
that  had  been  bought  by  a  different  one.  When  the  former 
complained  of 'the  overcharge  shown  in  the  monthly  state- 
ment rendered  him,  Mr.  Hunt  was  disturbed,  not  so  much 
at  the  possible  loss  of  the  sum  involved  as  by  the  feeling 
that  a  customer  might  consider  him  dishonest  rather  than 
unbusinesslike.  His  annoyance  was  further  increased  by 
being  unable  at  times  to  determine  who  was  the  purchaser. 

OMITTED  ENTRIES 

One  day  a  customer  who  wished  to  settle  his  account 
called  attention  to  the  omission  of  a  charge  for  goods  bought 
on  credit  early  in  the  month.  His  inability  to  recall  the 
details  of  the  purchase  or  its  total  showed  Mr.  Hunt  once 
more  the  need  for  a  better  system. 

A  complaint  within  a  day  or  two  from  another  customer 
that  his  monthly  statement  showed  no  credit  for  a  cash 
payment  on  account  made  the  previous  week,  confirmed 
Mr.  Hunt's  resolution  to  take  up  at  once  the  matter  of 
employing  business  methods. 


6  WALSH'S   BUSINESS   ARITHMETIC 

A  BETTER  WAY 

He  called  upon  Edward's  teacher  of  commercial  subjects 
(Mr.  Brown),  and  asked  him  if  he  could  suggest  a  method 
of  keeping  accounts  that  Edward  could  handle  in  the  short 
time  that  he  was  able  daily  to  devote  to  the  store.  Mr. 
Hunt  stated  that  neither  he  nor  his  two  regular  clerks  had 
had  any  experience  in  real  bookkeeping,  and  that  his  credit 
transactions  were  too  few  in  number  to  warrant  the  em- 
ployment of  an  experienced  bookkeeper.  He  said,  too,  that 
he  had  begun  to  realize  the  need  of  the  possession  of  more 
information  about  business  conditions  than  he  could  get 
from  a  ledger  that  showed  merely  the  store's  dealings  with 
a  few  customers. 

Mr.  Brown  explained  the  advisability  of  including 
among  the  ledger  accounts  one  showing  Mr.  Hunt's  relation 
to  the  business,  a  cash  account,  a  merchandise  account,  one 
giving  the  expense  of  conducting  the  business,  and  one 
with  each  individual  or  firm  from  whom  goods  were  pur- 
chased on  credit. 

He  showed  also  that  the  proper  keeping  of  some  of  the 
foregoing  accounts  would  require  the  employment  of  the 
double-entry  method,  the  advantages  of  which  he  briefly 
stated. 

He  recommended  the  use  of  a  journal  daybook,  in  which 
transactions  are  entered  in  the  order  of  their  occurrence. 
In  the  case  of  a  complaint  that  goods  had  been  charged  to 
a  person  other  than  the  purchaser,  a  reference  to  the  day- 
book would  supply  the  name  of  the  latter. 

The  advantages  of  journali/ing  the  entries,  as  a  prelim- 
inary to  their  transfer  to  the  ledger,  were  explained. 

WRITTEN   EXERCISE 

Make  out  the  bill  rendered  to  John  McKeon  by  Hiram 
Hunt  on  May  1,  1920  for  the  six  articles  purchased  by  the 
former  on  that  day. 


RECORDING    BUSINESS    TRANSACTIONS 


A  RECORDING  REGISTER 

Mr.  Brown  stated 
that  the  keeping  of 
the  books  could  easily 
be  done  by  Edward  in 
the  time  he  was  then 
giving  the  store.  The 
important  thing  was 
to  put  him  in  posses- 
sion of  all  the  data 
required  to  make  the 
entries.  These  de- 
tails, Mr.  Brown  said, 
could  best  be  supplied 
by  a  register  that  would  record  every  transaction,  giving 
the  sum  involved  and  its  character,  distinguishing  each  as 
either  a  sale  for  cash,  a  sale  on  credit,  a  cash  payment  made 
at  the  store  for  goods  previously  purchased,  or  a  purchase 
of  goods  by  the  store  on  credit. 

He  showed  Mr.  Hunt  that  the  employment  of  a  register 
in  which  every  transaction  was  "rung  up"  would  prevent 
an  omission  to  charge  a  customer's  account  with  goods  sold 
or  a  neglect  to  give  him  credit  for  a  payment  made. 


THE  INVENTORY 

Mr.  Brown  stated  that  the  ledger  account  which  should  be 
kept  with  the  proprietor,  Mr.  Hunt,  would  require  that 
an  inventory  should  be  made  to  determine  the  condition  of 
the  business  on  the  day  the  new  system  was  commenced,  by 
ascertaining  the  amount  of  cash  on  hand,  the  value  of  the 
stock  and  fixtures,  and  the  condition  of  unsettled  accounts. 

As  the  new  books  were  to  be  opened  on  June  1,  an  inven- 
tory was  made  as  of  the  close  of  business  on  May  31.  The 
cash  in  the  safe  was  found  to  be  $61.14,  and  that  in  the 
bank  $2284.75,  a  total  of  $2345.89.  The  value  of  the  mer- 


8 


WALSH'S    BUSINESS    ARITHMETIC 


chandise  was  taken  to  be  $1836.54,  and  that  of  the  fixtures 
$1372.50.  There  was  a  balance  of  $147.85  due  by  J.  H. 
Richards  and  one  of  $137.84  payable  to  R.  A.  Black. 

The  total  assets  (resources)  were  thus  found  to  be  $5702.78, 
and  the  liabilities  (debts)  $137.84,  showing  a  balance  of 
$5564.94,  which  constituted  the  net  resources. 

The  following  is  the  first  entry  in  the  journal  daybook,  the 
statement  of  the  assets,  of  the  liabilities,  and  of  the  balance, 
covering  the  daybook  portion.  In  making  this  part  Edward 
did  not  use  the  money  columns,  confining  all  the  details  to 
the  space  to  the  left. 

Jun.  1,  1920  (p.  1) 


Statement  of  the  assets  and  liabilities  at  the 

beginning  of  business  to-day 

Assets 

V 

Mdse.  as  per  inventory                       1836.54 

V 

Fixtures,  etc.  (see  list)                         1372.50 

v/ 

Cash  on  hand  (and  in  bank)               2345  .  81) 

v/ 

Due  from  J.  H.  Richards                      147  .  85 

5702.78 

Liabilities 

V 

DueR.  A.  Black                                    137.84 

V 

Net  Resources                                     5564.94 

5702.78 

2 

Mdse. 

1836 

54 

5 

Fixtures 

1372 

50 

6 

Cash 

2345 

89 

10 

J.  H.  Richards 

147 

85 

11 

R.  A.  Black 

137 

1 

Hiram  Hunt 

5564 

JOURNALIZING 

The  form  and  the  details  of  the  first  entry  were  suggested 
by  Mr.  Brown,  who  recommended  that  the  fixtures  should 
be  made  a  separate  item  in  the  inventory,  and  that  the 
lioiild  contain  a  Fixture  Account. 

He  showed  Edward  that  in  the  journal  entry  the  assets 
should  appear  as  debits  and  the  liahililies  as  credits,  the 


RECORDING   BUSINESS   TRANSACTIONS 


amount  of  the  net  resources  being  credited  to  an  account 
that  should  be  opened  with  Mr.  Hunt,  the  proprietor. 

In  writing  the  journal  portion  Edward  was  careful  to 
insert  the  amount  of  each  debit  in  the  first  money  column, 
and  that  of  each  credit  in  the  second  money  column.  As  he 
journalized  each  daybook  item,  he  placed  a  check  mark  (V) 
before  the  latter.  When  he  completed  the  journal  entry  he 
tested  the  correctness  of  his  figures  by  finding  the  sum  of  the 
debits  and  of  the  credits,  and  comparing  the  two  results. 

The  next  task  was  the  making  of  the  ledger  entries  ("post- 
ing") called  for  by  the  inventory.  These  are  shown  in  the 
following : 


FIRST  LEDGER  ENTRIES 
HIRAM  HUNT 


(P-  1) 


1920 

Jun. 

1 

Investment 

1 

p564 

!)t 

(p.  2) 


MERCHANDISE 


1920 
Jun. 

1 

Inventory 

1  J1836 

54 

FIXTURES 


(p.  5) 


1920 

Jun. 

(p.  6) 

1 

Value 
(See  list) 

1    |l372 

50 

!& 

iSH 

1 

1920 

Jun. 

1 

On  hand 

i  1*. 

89 

(P.  10) 


J.   H.   RICHARDS 


1920 

Jun. 

i 

Balance 

> 

147  85 

[ 

R.   A.  BLACK 


(p.  ID 


I 

1920 

Jun. 

1 

Balance 

'|187 

84 

10  WALSH'S   BUSINESS   ARITHMETIC 

STARTING  THE  NEW  LEDGER 

Edward  made  the  account  with  the  proprietor  the  first 
one  in  the  new  ledger,  writing  "HIRAM  HUNT"  at  the  top 
of  page  1.  Since  the  latter's  name  appeared  in  the  inven- 
tory among  the  credit  items,  he  first  wrote  5564.94  in  the 
credit  money  column.  In  the  first  journal  column,  on  a  line 
with  this  item,  he  wrote  the  ledger  page.  He  then  wrote 
"Investment"  to  specify  the  character  of  the  item,  after 
which  he  inserted  the  date.  He  completed  the  posting  of 
this  item  of  the  inventory  by  writing  1,  the  journal  page, 
in  the  ledger  column  to  the  left  of  the  money  one.  This 
he  did  to  facilitate  a  reference  to  the  journal  daybook  entry 
should  it  become  necessary. 

He  opened  the  ledger  accounts  called  for  by  the  other 
items  of  the  journal  entry,  in  the  order  in  which  they  ap- 
peared in  the  latter,  writing  MERCHANDISE  at  the  top 
of  page  2.  Noting  that  the  journal  specified  a  debit  entry, 
he  made  it  on  the  debit  side  of  the  page,  the  left  half,  pro- 
ceeding in  the  manner  followed  in  entering  the  Hunt  item. 

Because  of  the  likelihood  that  the  number  of  merchan- 
dise transactions  would  be  large,  he  left  pages  3  and  4 
blank  for  later  uses,  and  opened  the  FIXTURES  account 
on  page  5.  Here  he  entered  the  required  debit,  and 
then  opened  the  CASH  account  on  page  6.  After  mak- 
ing the  necessary  credit  entry,  he  left  three  blank  pages  and 
opened  accounts  with  J.  H.  Richards  and  R.  A.  Black,  respec- 
tively, on  pages  10  and  11,  and  made  the  proper  entries. 

This  work  he  completed  before  school  hours  on  June  1. 

A  DAY'S   TRANSACTIONS 

In  accordance  with  Mr.  Hunt's  orders,  each  of  the  fifty- 
.-i\  transactions  of  June  1  was  "rung  up"  on  the  register. 
This  recorded  the  number  of  the  transaction,  its  amount, 
the  date,  a  letter  to  denote  the  person  by  whom  it  was 
handled,  and  its  classification  under  one  of  five  types,  indi- 
cated as  follows: 


RECORDING   BUSINESS   TRANSACTIONS 


11 


*  An  ordinary  sale  for  cash 

Pd.  A  cash  payment  made  by  the  store 

Rec.  Cash  received  to  be  credited  to  a  debtor 

Ch.  A  sale  made  on  credit 

Bt.  A  credit  purchase  by  the  store 

Transactions  registered  by  Mr.  Hunt  were  denoted  by 
A,  those  by  the  two  clerks  by  B  and  C,  respectively. 

Of  the  day's  transactions,  forty-eight  were  cash  sales; 
the  other  eight  were  the  following,  numbered  in  the  order 
of  their  occurrence: 

1  Payment  of  June  rent  (check)  $125. — 

3  Sale  to  H.  A.  Gaynor  on  a/c  9 . 08 

6  Payment  of  freight  bill  (check)  19 . 44 

9  Check  received  from  J.  H.  Richards        147.85 

11  Purchase  of  sugar  on  account  515.20 

18  Payment  to  R.  A.  Black  (check)  137.84 

£1  Bank  deposit  207.85 

24  Payment  of  expressage  (cash)  1 . 50 

THE  RECORD   STRIP 

Each  of  these  was  recorded  in  its  appropriate  column  on 
the  strip.  The  following  portion  shows  these  eight,  and 
includes  a  few  of  the  cash  sales: 


ft 
2-  5.75-B 
4-  3.94-B 
5-10.  87-C 
7-     .95-B 
etc.  etc. 

PD. 

1-125.  00-A 
6-  19.44-A 
18-137  .  84-A 
21-207.  85-A 
24-     1.50-C 

REC. 

9-147.  85-A 

CH. 

1   3-9.08-B 

BT. 

11-515.20-A 

THE  CARDS 

Besides  making  the  foregoing  records  on  the  strip,  the 
register  printed  a  card  in  connection  with  each  transaction. 
On  the  following,  which  was  issued  in  connection  with  the 
rent  payment,  the  register  placed  this  heading: 


WALSH'S    BUSINESS    ARITHMETIC 


Pd.     A     125.00    0001     Jim- 1-20 


Mr.  Hunt,  who  made  the 
record,  noted  on  the  card,  for 
the  information  of  the  book- 
keeper, that  the  disbursement  was  a  payment  of  rent  made 
by  check,  and  placed  the  card  in  a  drawer. 

The  card  for  transaction  2,  a  cash  sale,  was  given  to  the 
customer.  It  contained  this  heading: 

*     B     5.75     0002     Jun-1-20 

In  connection  with  the  third  transaction,  a  credit  sale, 
the  register  printed  the  heading  at  the  top  of  a  bill  and  its 
carbon  duplicate  in  this  form: 

Clerk  B  filled  in  the 
details  as  shown  here- 
with, gave  Mr.  Gaynor 
the  bill,  and  placed  the 
duplicate  in  a  drawer  of 
the  register. 

Transactions  4  and  5, 
cash    sales,    were    regis- 
tered in  the  same  way  as 
No.    2,    and    the    cards 
given  to  the  purchasers. 
Mr.  Richards,  transaction  9,  not  having  sent  with  his 
check  the  bill  it  was  intended  to  settle,  Mr.  Hunt  registered 
the  heading  on  a  blank  receipt  and  its  duplicate,  which  he 
filled  out  in  the  form  shown  herewith: 


Ch.     B    9.08    0003    Jim -1-20 


Hiram  Hunt 


Sold  to 


24  ib.  Butter 
5  "  Coffee 
Amount  of  this  purchase 


.32 

.28 


Rec.     A     147.85    0009    Jun-1-20 


He  mailed  the  origi- 
nal to  Mr.  Richards, 
and  placed  in  the 
drawer  the  carbon  du- 
plicate, noting  on  the 
latter  "By  check." 
If  Mr.  Richards  had  inclosed  the  bill,  this  would  have  been 

receipted  and  returned,  and  the  transaction  recorded  on  a 

card. 


Received  of  J.  II.  Richards 

One  Hundred  Forty-seven  85/100  Dollars 

in  full  of  account  to  date. 

Hiram  Hunt 


RECORDING    BUSINESS    TRANSACTIONS          13 

The  bank  deposit,  transaction  21,  while  not  being  one 
calling  for  an  entry  in  the  daybook,  was  "rung  up"  to 
account  for  the  withdrawal  of  cash  from  the  drawer  and  the 
safe.  It  appeared  thus: 

Pd    A     207.85     0021     Jun-1-20 

On  the  card,  which  Mr.  Hunt  placed  in  the  drawer,  he 
noted 

"Deposit:  Cash,  $60;  Check,  $147.85" 

THE  BOOKKEEPER 

When  Edward  reached  the  store,  after  school,  he  first 
counted  the  cash  in  the  register,  which  he  found  to  be 
$37.12.  He  then  examined  the  register  slip  to  ascertain  the 
number  of  transactions  recorded,  and  their  character.  He 
learned  that  there  were  up  to  that  time  44  in  all,  36  of 
which  were  sales  for  cash,  amounting,  according  to  the 
register,  to  $37.48.  To  this  he  added  $21.14,  which  had 
been  placed  in  the  drawer  in  the  morning  for  change, 
which  made  a  total  of  $58.62.  From  this  he  deducted 
$1.50,  cash  paid  for  expressage,  leaving  $57.12  to  be  ac- 
counted for. 

The  difference  between  this  sum  and  the  $37.12  in  the 
drawer  showed  that  $20  had  been  taken,  presumably  for 
the  deposit.  An  examination  of  the  safe,  in  which  $40  had 
been  left  in  the  morning,  showed  that  this  had  been  used 
to  make  up  the  $60  deposited  in  cash. 

Finding  the  money  correct,  Edward  proceeded  to  make 
the  entries  in  the  journal  daybook.  As  a  preliminary, 
he  collected  the  necessary  data:  cards,  bills,  bank  book, 
check  book,  etc. 

Taking  up  the  first  transaction  recorded  on  the  strip, 
the  payment  of  $125,  he  learned  from  the  card  that  it 
covered  the  June  rent,  and  that  it  had  ,^>een  made  by  check. 
From  the  check-book  stub  he  found  that  a  check  for  that 
amount  had  been  drawn,  which  had  been  correctly  deducted 
from  the  previous  balance. 


14 


WALSH'S   BUSINESS   ARITHMETIC 


He  then  made  the  following  entry  of  the  first  transaction, 
using  a  ditto  mark  (")  to  show  that  the  date  was  the  same 
as  that  of  the  previous  entry  (June  1)  : 


\/        Paid  rent  for  June 
Expense 

Cash 


125.— 


125 


125 


The  first  line  constitutes  the  daybook  portion.  This  he 
"journalized"  in  the  form  shown  in  the  next  two  lines. 
He  first  entered  125. — ,  the  amount,  in  each  of  the  two 
money  columns,  once  as  a  debit  and  once  as  a  credit.  The 
transaction,  involving  an  expenditure  of  cash,  requires  that 
the  Cash  account  in  the  ledger  be  credited  with  this  sum. 
The  journal  entry,  therefore,  placed  "Cash"  in  the  credit 
place.  Inasmuch  as  expenditures  for  such  items  as  freight, 
expressage,  postage,  taxes,  clerk  hire,  rent,  etc.,  were  to 
be  entered  in  the  ledger  under  the  general  title  of  "  Expense," 
Edward  debited  the  Expense  account  with  $125. 

He  began  the  debit  entry  item  close  to  the  first  vertical 
line  and  the  credit  entry  about  an  inch  to  the  right. 

Finding  from  the  record  strip  that  transaction  2  was  a 
cash  sale,  Edward  went  to  the  next.  From  the  carbon  dupli- 
cate placed  in  the  drawer,  he  obtained  the  details,  for  the 
daybook  portion,  which  are  given  in  the  first  three  lines 
of  the  following  entry: 


V/    Sold  H.  A.  Gaynor  on  account 

24  Ib.  Butter       .32  7.Q8 

5  "  Coffee        .28  1.40 

H.  A.  Gaynor 

M.lse. 


9.08 


In  journalizing  it,  he  wrote  "9.08"  twice,  as  in  the  pre- 
ceding entry.  On  Jhe  first  line  (the  debit  one)  he  wrote 
"H.  A.  Gaynor,"  whose  ledger  account  was  to  be  debited 
with  $9.08  for  goods  bought.  On  the  credit  line,  he  wrote 
"Mdse.,"  the  ledger  account  of  which  was  to  be  credited. 


RECORDING    BUSINESS    TRANSACTIONS 


15 


Transactions  4  and  5,  cash  sales,  were  passed  over,  and 
after  Edward  had  verified  the  extension  of  the  freight  bill, 
examined  the  check-book  stub,  etc.,  he  made  the  following 
entry  of  transaction  6: 


Paid  freight 
Expense 

Cash 


19.44 


19 


1944 


The  following  are  the  entries  for  the  remaining  transac- 
tions other  than  the  sales  for  cash: 


\/      Received  check  from  J.  H.  Richards 

in  full  of  account  147 . 85 


Cash 


J.  H.  Richards 


>/      Bought  from  Franklin  Refinery  on  a/c 

25  bbl.  Sugar,  as  per  invoice  515.20 


Mdse. 


Franklin  Refinery 


Paid  R.  A.  Black  in  full  of  account  to 

date  137.84 

R.  A.  Black 

Cash 


\f      Paid  Cash  for  expressage 
Expense 

Cash 


1  .  50 


147 

85 

147 

85 

515 

20 

515 

20 

137 

84 

137 

8-4 

1 

50 

1 

50 

When  business  was  over  for  the  day,  the  register  showed 
that  the  number  of  cash  sales  was  48,  totaling  $63.15.  The 
following  was  the  final  entry  for  Jun.  1 : 


Received  from  48  cash  sales,  as  per 

register 
Cash 

Mdse. 


63.15 


15 


6315 


16 


WALSH'S   BUSINESS    ARITHMETIC 


POSTING  THE  DAY'S  TRANSACTIONS 

While  waiting  for  remaining  sales  to  enable  him  to  make 
the  final  daybook  entry,  the  cash  sales  for  June  1,  Edward 
began  to  make  the  ledger  entries.  Turning  to  the  journal 
portion  of  the  first  transaction  he  found  it  to  be: 

12        Expense  II    1251—    II 

6  Cash  125 


which  required  that  the  Expense  account  in  the  ledger  be 
debited  with  $125,  and  that  the  Cash  account  be  credited  with 
the  same  sum.  Since  the  ledger  did  not  as  yet  contain  the 
former  account  he  opened  one  on  page  12,  and  entered  the  re- 
quired debit,  inserting  in  the  journal  "12,"  the  ledger  page 
of  the  Expense  account.  He  completed  the  posting  of  this 
transaction  by  crediting  the  Cash  account  with  $125,  and 
inserting  in  the  journal  "6,"  the  ledger  page  of  the  Cash 
account. 

He  then  took  up  the  other  journal  entries  in  regular  order, 
opening  accounts  with  H.  A.  Gay  nor  and  Franklin  Refinery 
on  pages  13  and  14,  respectively. 

T.  "  accounts  appeared  as  follows  after  the  posting 

of  the  las.  ?tion  of  the  day.  A  line  was  drawn  under 

the  accour-  H.  Richards  and  one  under  that  of  R.  A. 

Black  to  show  ti^at  each  had  been  settled. 


THE  LEDGER  PAGES 
HIRAM  HUNT 


(p.  1) 


IIP 


|  11920 
Tun. 


Investment 


(p.  2) 


MERCHANDISE 


1920 

JlIM. 


Inventory 
Frank.  Ref. 


H.  A.  Gaynor 
Cash  Sales 


908 


RECORDING   BUSINESS   TRANSACTIONS          17 

FIXTURES  (p.  5) 


1920 

Juu. 

I 

Value 

1 

1372 

50  ! 

1 

(p.  6) 

1920 

Jun. 

« 

I 
1 
1 

On  hand~ 
J.  H.  Richards 
Sales  for  day 

7 

i 
i 

CASH 

2345 
147 
63 

89 
85 
15 

1920 
Jun. 

1 
1 
1 
1 

Rent 
Freight 
R.  A.  Black 
Express 

1 
1 
1 
1 

125 
19 
137 
1 

H- 
81 
50 

(p.  10)                                 J.  H.  RICHARDS 

1920 

Jun. 

1 

Balance 

i 

147 

85 

1920 
Jun. 

1 

Cash 

HI147 

85 

R.  A.  BLACK                                    (p.  11) 

1920 

Jun. 

1 

Cash 

i 

137 

84 

Jun. 

1 

Balance 

1      137 

84 

(p.  12)                                           EXPENSE 

1920 

Jun. 

« 

« 

1 
1 
1 

Rent 
Freight 
Express 

i 
i 
i 

125 
19 
1 

44 
50 

H.  A.  GAYNOR                                  (p.  13) 

1920 

Jun. 

1 

Mdse. 

i 

908 

(p.  14)                            FRANKLIN  REFINERY 

11920 

Jun. 

1 

Mdse. 

4 

515 

20 

18 


WALSH'S   BUSINESS   ARITHMETIC 


ORAL  EXERCISES 

1.  State  why  each  item  (a)  on  the  debit  side  of  the  mer- 
chandise account  is  entered  therein.     (6)  On  the  credit  side. 

2.  What  does   (a)  the   debit   side   of  the  cash  account 
show?     (6)  The  credit  side? 

3.  How  would  you  journalize  (a)  the  purchase  of  a  plat- 
form scales  from  the  Fairbanks  Company  on  credit?    (6)  The 
purchase  of  2000  postage  stamps  for  cash?    (c)  The  payment 
by  check  of  a  bill  for  electric  light?     (d)  The  purchase  of  10 
tons  of  coal  on  credit? 

4.  (a)  What   is   shown   by   the   difference   between   the 
totals  of  the  two  sides  of  the  cash  account?     (6)  How  can 
the  correctness  of  this  difference  be  determined?     (c)  Which 
side  must  always  have  smaller  total?    Why? 

THE  BANK  ACCOUNT 

Mr.  Hunt  kept  his  account  with  the  Newaygo  County 
Bank  on  the  stubs  of  the  check  book,  as  shown  on  another 
page. 

In  making  a  deposit  he  filled  out  a  slip  like  the  accompany- 
ing form,  which  he  sent 
to  the  bank  with  the 
money  and  the  bank 
book.  When  the  mes- 
senger returned,  Mr. 
Hunt  examined  the 
book  to  see  that  the 
proper  entry  had  been 
made;  then,  on  the  stub 
he  added  $207.85,  the 
amount  of  the  deposit, 
to  the  previous  balance, 
$2159.75,  making  a  total 
of  $2367.60  to  his  credit 
in  the  bank. 


Deposited  in 
The  Newaygo  County  Bank, 

White  Cloud,  Mich, 
by  Hiram  Hunt 

Address:  4  Court  Square. 

Jun.  1,  1920 


Bills 
Coin 

Chrck 


List  each  check  separately 


40 

20 

147 


207 


RECORDING   BUSINESS   TRANSACTIONS 


a 


1  s 


S     & 
>     O 

o 

o 


w 


19 


2        |1 

£5  *»    8 

JHIJ 


i 


20 


WALSH'S  BUSINESS  ARITHMETIC 


When  Mr.  Hunt  made  out  check  No.  458  in  payment 
of  the  June  rent,  he  detached  it,  leaving  in  the  book 
the  portion  on  the  left,  called  the  stub.  On  the  latter 
he  wrote  the  name  of  the  person  in  whose  favor  the 
check  was  drawn  (the  payee),  the  item  covered  by  the 
payment,  its  amount,  and  then  deducted  this  amount 
from  the  previous  balance,  2284.75.  He  brought  down 
the  remainder,  2159.75,  to  the  stub  for  check  No.  459. 

WRITTEN  EXERCISES 

1.  On  a  sheet  of  paper  of  the  proper  size,  make  a 
copy  of  the  next  two  checks  with  their  accompanying 
stubs.     Fill  out  one  check  to  cover  a  freight  payment, 
and   the   other   to   settle   Mr.   Hunt's   account   with 
R.  A.  Black.     Use  the  proper  number  for  each,  and 
insert    the    amounts    specified    in    the    entries.     Fill 
out  each  stub  properly,  inserting  in  the  last  one  the 
deposit  of  $207.85,  made  before  the  check  is  drawn. 

2.  (a)  How  much  cash  should  Mr.  Hunt  have  in  the 
store  at  the  close  of  business  on  Jun.  1  ?    (6)  What  should 
be  his  bank  balance?     (c)  Compare  the  sum  of  (a)  and 
(6)  with  the  difference  between  the  Dr.  and  the  Cr.  side 
of  the  cash  account  in  the  ledger. 


(p.  16) 


BALANCING   AN  ACCOUNT 
WM.  WINKLE 


1920 

1920 

Jun. 

2 

.  To  Mdse. 

2 

27 

65 

Jun. 

20 

By  Cash 

20 

50 

— 

" 

8 

«       u 

9 

8 

43 

" 

27 

41           it 

32 

u 

_ 

it 

10 

"       " 

12 

19 

64 

" 

30 

"  Bal. 

28 

10 

n 

15 

".      " 

18 

37 

53 

44 

23 

44                44 

27 

9 

85 



in:; 

10 

!().•{ 

i<> 

JuL 

1 

To  Bal. 

28 

10 

» 

RECORDING  BUSINESS  TRANSACTIONS      21 

3.  Find  (a)  the  total  of  the  Jun.  1  journal  debits, 
including  those  of  the  inventory.  (6)  The  total  of 
the  credits,  (c)  The  total  of  the  debits  in  the  ledger 
entries,  (d)  The  total  of  the  credits. 

On  the  first  day  of  July  Edward  balanced  the  June  ac- 
counts. The  method  is  shown  in  the  foregoing  ledger  ac- 
count with  Wm.  Winkle.  Noting  that  the  Dr.  side  was 
the  greater,  he  wrote  under  the  former  its  total,  103.10, 
and  placed  the  same  total  as  the  footing  of  the  Cr.  side, 
writing  it  on  a  line  with  the  other  total. 

He  then  made  the  entry  "By  Balance,"  writing  this  in  red 
ink,  also  the  date,  "Jun.  30,"  and  the  amount  of  the  balance, 
"28.10."  This  he  ascertained  by  deducting  the  sum  of  $50 
and  $25  from  $103.10.  He  then  drew  a  line  under  both 
totals,  closing  the  account,  which  he  reopened  by  the  entry 
of  Jul.  1,  "To  Bal.,  28.10,"  which  is  the  amount  due  from 
Wm.  Winkle. 

He  then  mailed  to  Mr.  Winkle  the  following  monthly 
statement,  omitting  the  details  of  the  purchases,  since  Mr. 
Winkle  had  received  a  bill  with  each. 


Mr.  WM.  WINKLE 


MONTHLY  STATEMENT 

WHITE  CLOUD,  MICH.,  Jul.  1,  1920 

In  account  with  HIRAM  HUNT 

General  Merchandise 

4  Court  Square 


1920 

Jun. 

2 

To  Mdse.  as  per  bill  rendered 

27 

65 

8 

"        "       "     "     "          " 

8 

43 

10 

«        «       «     «     «          « 

19 

64 

15 

«        «       «     «     <(          « 

37 

53 

23 

<<        «       «    «     «          « 

9 

85 

103 

10 

Cr. 

Jun. 

20 

By  Cash 

50 

— 

27 

«       « 

25 

— 

75 

— 

Due 

28 

10 

(p.  10) 


WALSH'S  BUSINESS  ARITHMETIC 

ANOTHER  LEDGER  PAGE 
J.   H.  RICHARDS 


1920 

1920 

Jun. 

8 

To  Mdse. 

9 

13 

48 

Jun. 

18 

By  Mdse. 

21 

48 

66 

" 

13 

"       " 

15 

6 

86 

" 

28 

««       « 

33 

87 

95 

" 

16 

«       « 

19 

27 

95 

" 

20 

«       « 

23 

42 

63 

« 

27 

"       " 

32 

18 

04 

" 

30 

"  Bal. 

27 

65 

__ 

130 

6J_ 

136 

61~ 

nrn 

Jul. 

1 

By  Bal. 

[27 

65~ 

In  balancing  this  account,  Edward  observed  that  the 
credit  total  was  in  excess  of  that  of  the  debits.  This  re- 
quired a  balance  entry  in  the  debit  column,  for  which  he  left 
a  line.  The  final  debit  total,  therefore,  appeared  two  lines 
below  the  last  debit  entry;  on  this  line,  on  the  credit  side, 
he  entered  136.61,  and  wrote  it  on  the  debit  side  also.  Add- 
ing the  debits  and  subtracting  them  from  lQ&06~4n  one 
operation,  he  entered  the  balance,  27.65,  in  red  ink,  and  also 
the  date  and  the  word  "Bal."  He  closed  it  by  drawing  the 
necessary  lines,  and  reopened  it  by  entering  a  credit  balance 
of  27.65. 

When  a  bill  was  received  from  Mr.  Richards,  on  Jul.  2, 
Edward  compared  it  with  the  account,  and  notified  Mr. 
Hunt  to  send  a  check  in  settlement. 

WRITTEN  PROBLEMS 

1.  Make  a  copy  of  the  foregoing  account,  balance, 
etc.,  as  it  appears  in  the  ledger  of  J.  H.  Richards. 

Write  the  heading  "Hiram  Hunt."  Credit  this  account  with  the  items 
that  appear  as  debits  in  Mr.  Hunt's  ledger,  and  vice  versa.  Insert  journal 
pages  other  than  those  found  in  Mr.  Hunt's  ledger. 

2.  Make  out  the  monthly  statement  sent  to  Mr. 
Hunt  by  J.  H.  Richards. 

3.  Write  the  check  sent  by  Mr.  Hunt  in  settlement 
of  the  account. 


RECORDING  BUSINESS  TRANSACTIONS      23 

4.  (a)  Find  the  total  weekly  pay  of  73  graduates  of 
a  boys'  technical  school  who  receive  weekly  compen- 
sation as  follows  during  the  first  year  of  employment: 

2  receive  $6  16  receive  $9 

21  7  8  10 

20  8  6  11 

(6)    What  is  the  average  weekly  pay? 

5.  Find  the  average  weekly  pay  of  graduates  in 
the  second  year  of  employment  who  received  weekly 
compensation  as  follows : 

8  received  $7  11  received  $11 
19                   8  11  12 
10                   9                       9  13 

9  10  7  14 

6.  Find  the  average  weekly  pay  of  graduates  in  the 
third  year  of  employment  who  receive  weekly  com- 
pensation as  follows : 

4  received  $10  16  received  $15 

6                    11  6                    16 

4                    12  10                    17 

9                    13  2                    18 

9         "         14  2         "         20 


CHAPTER  TWO 


SALES  SLIP 
No.  1     VII- 1-20 

W.  S.  Julius  &  Co. 
Sold  to 

Cash 


.06 


A   GIRL   IN    BUSINESS 

Miss   White  began   as   sales  girl   in  a  department 
store.     Her  first  customer  bought,  for  cash,  the  goods 

shown  on  the  accompanying 
sales  slip.  In  writing  this, 
Miss  White  made  a  carbon 
duplicate.  In  the  space  at  the 
bottom  of  the  slip  marked 
"Cash,"  Miss  White  wrote 
2.31,  the  total  of  the  trans- 
action, and  in  the  one  marked 
"Rec'd,"  she  wrote  5.—,  the 
denomination  of  the  bill 
handed  her  by  the  customer. 
She  then  sent  both  slips,  the 
$5  bill,  and  the  goods  to  the 
wrapper.  The  latter  compared 
the  duplicate  slip  with  the 
original,  and  the  latter  with 
the  articles.  Finding  every- 
thing correct,  she  placed  her  check  mark  on  the  original 
and  sent  the  two  slips,  with  the  $5,  to  the  cashier.  The 
latter  returned  the  duplicate  to  Miss  White  with  the 
change,  and  sent  the  original  ta  the  auditing  depart- 
ment. The  wrapper  made  the  goods  into  a  neat  parcel 

24 


3 

3  J$iu&  ffiovc&z,  .36 


/6 
33 
7^ 
/  06 
06 


CASH 

2.3! 


REC'D 

6.— 


CH'G. 


(  .0.1). 


RECORDING  BUSINESS  TRANSACTIONS      25 


and  sent  it  to  Miss  White,  who  gave  it  to  the  pur- 
chaser, together  with  the  duplicate  slip  and  the  change. 
To  be  certain  of  the  correctness  of  the  latter,  she 
counted  it  out  to  the  purchaser,  saying:  "2.31  and 
4,  2.35;  and  5,  2.40;  and  10,  2.50;  and  50,  3  dollars; 
and  2,  5  dollars";  handing  over,  as  each  item  was 
specified,  the  4  cents,  the  nickel,  the  dime,  the  half- 
dollar,  and  the  $2  bill,  supplied  by  the.  cashier. 

The  next  sale  was  a  credit  one.     This  is  shown  by 
the  entry  of  the  total  in  the 
space      marked       "Chg." 
(charge)  at  the  bottom  of 
the  slip. 

To  make  sure  that  the 
name  and  residence  of  the 
purchaser  were  correctly 
written,  they  were  read  to 
the  latter  by  Miss  White, 
from  the  slip.  This,  with 
the  duplicate  and  the 
goods,  was  sent  to  the 
wrapper.  The  original  slip 
after  being  checked  went 
to  the  charge  clerk,  and  the 
duplicate  with  the  parcel  to 
the  delivery  department. 


SALES  SLIP 

No.  2    VII-1-20 
W.  S.  Julius  &  Co. 
Sold  to 
Mrs.  J.  Carroll  Payne 
8502  Hamilton  Boulevard 

2  $0* 

w&wCa/          .23 

Z 

/    // 

// 

£5 

6  <3oa/ 

fa                   .05 

30 

/  86 

CASH 

REC'D           CH'G. 

1.86 

C.O.D. 

WALSH'S  BUSINESS  ARITHMETIC 


A   GIRL'S  DAILY   SALES 

On  a  daily  sales  card,  Miss  White  entered  the  amount 

of  each  sale,  classify- 
ing it  as  cash,  charge, 
or  C.O.D.  At  the 
close  of  business  she 
entered  the  total  of 
each  type,  the  grand 
total,  and  the  number 
of  sales  made.  This 
card  went  to  the  de- 
partment of  audits. 

In  order  to  deter- 
mine how  she  was  suc- 
ceeding in  her  work, 
Miss  \Vhite  kept  a 
memorandum  of  the 
number  of  her  daily 
sales  and  their  total. 
She  was  gratified  to  perceive  that  her  promptness,  cour- 
tesy, knowledge  of  the  stock,  etc.,  enabled  her  to  make 
a  steady  increase  in  the  number  of  transactions  she 
was  able  to  handle  in  a  day. 

WRITTEN  PROBLEMS 

1.  From  Miss  WTiite*s  Daily  Sales  slip  for  Jul.  1, 
find  the  total  of  the  sales  (a)  made  for  cash,  (6)  charged, 
(c)  C.O.D.,  and  (d)  the  grand  total. 

2.  From  the  accompanying  list  of  the  sales  made 
during  the  week  ended  Jul.  6,  by  the  five  girls  at  the 


DAILY  SALES 

Date  VII-1-20              Sold  by  M.  White 

CASH               CH'G.            C.O.D. 

No.    Am't.        No.     Am't.       No.  Am't. 

1 

2 

31 

1 

1 

86 

1 

1 

35 

2 

79 

2 

1 

27 

2 

1 

65 

3 

15 

3 

3 

1 

87 

4 

3 

48 

4 

4 

5 

2 

67 

5 

5 

6 

1 

10 

6 

6 

7 

50 

7 

7 

8 

25 

8 

8 

9 

3 

11 

9 

9 

10 

10 

10 

11 

11 

11 

12 

12 

12 

Tot.      (a)                   (6)                   (c) 

No.  of  Sales  U             Grand  Tot.      (d) 

RECORDING  BUSINESS  TRANSACTIONS      27 

notion  counter,  find  the  weekly  sales  of  each,  (a)  to 
(e)\  the  total  sales  for  each  day,  (/)  to  (fc);  and  the 
total  sales  of  notions  for  the  week,  (/). 


DAY 

Miss  W. 

Miss  V. 

Miss  U. 

Miss  T. 

Miss  S. 

TOT. 

Monday 

22 

.36 

38 

.75 

32 

.63 

30 

.48 

36 

.12 

(/) 

Tuesday 

11 

.17 

19 

.05 

17 

.38 

15 

.72 

18 

.69 

(</) 

Wednesday 

43 

.82 

31 

.56 

27 

.73 

29 

.84 

28 

.11 

(A) 

Thursday 

36 

.09 

24 

.12 

22 

.34 

25 

.56 

23 

.89 

W 

Friday 

32 

.77 

19 

.45 

21 

.67 

20 

.90 

18 

.23 

tf) 

Saturday 

38 

.04 

32 

.78 

34 

.88 

30 

.76 

36 

.65 

(k) 

Totals  (a)         (6)         (c)         (d)         (e)  (I) 

Find  (I)  by  adding  the  line  totals  (/)  to  (k).  Check 
(1)  by  adding  the  column  totals  (a)  to  (e). 

3.  Miss  White's  weekly  pay  is  $6  plus  a  commission 
of  5%  on  sales  in  excess  of  $100.  What  did  she  re- 
ceive for  a  week  during  which  her  sales  amounted  to 
$184.25? 


METHOD 

$6  +  5  %  of  $84.25  ($184.25  -  $100.00)  =  $6  +  $4.21 
=  $10.21,  Ans. 


4.  Find  the  compensation  received  by  each  of  the 
other  girls  at  the  notion  counter  for  the  week  from 
Jul.  1  to  Jul.  6,  at  $6  plus  5%  on  sales  in  excess  of 
$100. 


28  WALSH'S  BUSINESS  ARITHMETIC 

THE  BILL  CLERK 

Miss  White's  quickness  at  figures  obtained  for  her 
a  promotion  to  a  place  in  the  dress  goods  department. 
Her  ability  to  fill  out  correctly  the  extensions  in  a 
sales  slip,  without  making  "side"  calculations,  enabled 
her  to  save  the  time  of  her  customers,  as  well  as  to 
make  in  a  day  a  larger  number  of  sales  than  were  made 
by  some  of  her  fellow  clerks  of  greater  experience. 

Her  next  promotion  was  to  a  place  in  the  office  of 
the  cashier,  to  check  up  the  extensions  on  the  sales 
slips.  From  this  she  went  to  the  billing  department. 

SIGHT  EXERCISES 

1.  Give  to  the  nearest  cent  the  extension  of  each 
of  the  following  items  in  a  bill: 

a  8    yd.  Muslin  @  6ff         6  8   yd.  Tape 

c  8 

t>  ftiz 

V    O/2 

g  4 

i  5 

ra24 


Cambric  "  QY2i      d  %          Cambric 

3^  "    Mohair 
Sateen  "  14}^     h  10  "    Cashmere       "  85  £ 


Cashmere         '  96  ^      j  2^  "  '  $&£ 

Twill  "  8K4      I  16  "    Sateen  "  $% 


Sateen  "  25  (f       n  25 


o  12X "  ;<  24^  p  iy4  "  Alpaca 

q  2      "  Padding  "  84ff  r  %     "  Padding          "  84ff 

s  2#    "  "  82^  t  4     "  Dress  Goods  ( 

11  X     "  Dress  Goods  "  42^f  o  3%  " 

w?2M    "  Cambric          "  19ff  z  64  "  Muslin 

y  36    "  Silk  "  99^f  z  99  "  Cashmere       ' 


2.    (a)  From  10  times  44,  take  %  of  44;    (6)  multi- 
ply 44  by  9& 


RECORDING  BUSINESS  TRANSACTIONS      29 
3.   Give  products: 

a  44  X  19%  b  44  X  25  c  44  X  24% 

d  44  X  24X  e  44  X  49%  /  44  X  99% 

g  32  x  19%  A  32  x  24%  i  32  X  99% 

MONTHLY  BILL  OF  A  DEPARTMENT  STORE 

The  following  is  the  heading  of  the  bill  rendered 
monthly  by  W.  S.  Julius  &  Co.  to  his  "Charge" 
customers : 

DATE,  Jul.  31,  1920  FOLIO  35814 

NAME,     Mrs.  J.  Carroll  Payne 

ADDRESS    8502  Hamilton  Boulevard,  Tucson. 

AMOUNT  OF  PAYMENT,  $ 

Tucson,  Ariz.,  Jul.  31,  1920 
W.  S.  Julius  &  Co. 

SOLD  TO  Mrs.  J.  Carroll  Payne 

8502  Hamilton  Boulevard. 


TERMS:  Settlements  required  the  first  part  of  each  month. 

When  the  bill  is  paid,  the  cashier  enters  the  sum  received 
on  the  coupon  at  the  top,  which  he  detaches  and  sends  to 
the  department  of  customers'  accounts.  He  then  receipts 
the  bill,  which  he  returns  to  the  customer. 

The. body  of  the  bill  contains  three  money  columns,  two 
for  the  debits  and  one  for  the  credits.  The  second  debit 
column  gives  the  total  of  the  purchases  of  the  day.  The 
credit  entries  are  made  in  red  ink. 


30  WALSH'S  BUSINESS  ARITHMETIC 

WRITTEN  EXERCISES 

Make  out  a  monthly  bill  covering  the  following 
purchases.  Fill  in  the  missing  items  (a)  to  (s).  Make 
yourself  a  purchaser  and  a  local  firm  the  seller. 


Date 

Amount 

Daily 
Total 

Credit 

Jul. 
1 

2 

6 

8 
10 
11 

13 
15 
18 

20 

27 

2  Paste                                           .20 
2  Ammonia                                    .23 
1  pr.  Scissors 
1   "       " 
6  Soap                                            .05 
1  yd.  Cretonne 
4  Towels                                        .  19 
VA  yd.  Padding                              .82 
Kdoz.  Plates                               2.70 
%    "         "                                     1.50 
1  yd.  Cretonne 
1  Wrapper 
1  Skirt 
3%  yd.  Dress  Goods                      .42 
6  Napkins                                      .05 
1  pr.  Hose 
3  doz.  Napkins                              .  35 
3%  yd.  Dress  Goods                   .42 
1  Wrapper 
4  yd.  White  Goods                        .20 
3  pr.  Hose  for 
2Ji  yd.  Cambric                             .19 
6  Handkerchiefs                            .35 
1  Smock 
S%  yd.  Embroidery                       .08 
1  Dress 

40 
46 
25 
45 
30 

1 

1 
1 

86 

(«) 

(/) 

to 

C0 

35 
05 

(n) 
(p) 

1 
3 

38 

58 

95 

38 
(a) 
(b) 

(d) 
(e) 

3 

95 
98 

(*) 

W 

1 

(*) 

(/) 
(«) 

1 
2 

29 
(a) 

75 

Total 
Less 
Due 

% 

(r) 

Paid  Aug.  S,  1920 
W.  S.  JULIUS  &  Co. 
by  M.  E.  K. 

W 

Do  not  use  the  price  column  when  a  single  article  is  bought;  write  the 
price  only  in  the  "amount"  column.  When  but  one  purchase  is  made  on 
any  day,  write  the  amount  only,  in  the  "daily  total"  column. 


RECORDING  BUSINESS  TRANSACTIONS      31 


CUSTOMER'S  RECEIPT 
DATE  VII-17-20    R  32748 
RECEIVED  OF  Mrs.  J.  Carroll  Payne 
ADDRESS    8502  Hamilton  Blvd. 


THE   CAREFUL  CUSTOMER 

Upon  the  arrival  of  each  purchase,  Mrs.  Payne 
examines  the  sales  slip  to  be  sure  that  she  has  received 
all  of  the  articles  charged  to  her  account.  She  then 
files  away  the  slips  until  the  arrival  of  the  monthly 
bill,  which  she  "checks"  by  means  of  the  slips. 

She  also  examines  the  credit  column  to  ascertain 
that  the  proper  reduc- 
tions have  been  made 
for  the  articles  re- 
turned, as  shown  by 
her  "  Customer's  Re- 
ceipts." 

When  she  finds  that 
goods  received  are  un- 
satisfactory or  un- 
necessary, she  notifies 
the  store  to  send  for 
them.  The  driver  gives 
her  a  receipt  in  the 
accompanying  form, 
which  is  a  carbon  copy 
of  the  "Call  Check" 
filled  out  by  the  driver  and  brought  by  him  to  the 
store  with  the  articles  returned. 

THE  OFFICE  ASSISTANT 

Miss  White's  desire  to  become  an  efficient  employee 
caused  her  to  devote  much  of  her  spare  time  to  a 
review  of  the  commercial  branches.  Now  that  she 
was  daily  brought  face  to  face  with  the  advantages  of 


RETAIN   THIS   RECEIPT   OF   GOODS 
RETURNED 


WHYRl 

CALL 


DEP'T.- 
ORDER  '. 

Paid  or  Charge          Check  Entry 

W.  S.  JULIUS  &  Co. 
per  T.  E.  B. 


WALSH'S  BUSINESS  ARITHMETIC 


training,  she  brought  a  new  interest  to  her  studies,  and 
the  latter  held  for  her  a  new  meaning. 

When,  one  day,  she  was  offered  the  position  of  office 
assistant  to  the  purchasing  agent  of  The  Harrison 
Company,  she  accepted  it,  feeling  competent  to 
perform  the  duties,  and  glad  of  the  opportunity  for 
more  varied  work  than  she  would  be  likely  to  get  in 
a  larger  business. 

THE   ORDER  BOOK 

One  of  her  duties  is 
to  make  stenographic 
notes  of  goods  to  be 
purchased,  and  to  fill 
out  the  necessary  order 
slips.  She  writes  each 
on  a  perforated  sheet 
of  the  order  book,  a 
carbon  copy  being 
made  on  a  page  re- 
maining in  the  book. 
When  the  bill  is  re- 
ceived, she  stamps  the 
date  on  the  order.  This 
she  also  does  when  the 


THE  HARRISON  CO. 

Office  of  the  Purchasing  Agent 

Happy  Valley,  Ariz. 

Nov.   16,   1921 
No.  5837 
Be  sure  to  place  this  order  number  on  your  bill. 


CM  CM 
CD  O> 


Messrs.  Barrett  and  Jones 
1364  Water  Street 

Cincinnati,  Ohio 


>  o 

O  2 


KINDLY  SHIP  BY  Freight 


6  2-in.  Brass  Valves 

2  3-in.  IBB 

2  Victor  Gate   " 


F247 
F600 


P  b 
u  w 

-  en 

d  8        ^ 

no  Purchasing  Agent. 

Mail  bills  in  duplicate  when  goods  are 

shipped 
Mail  statements  the  last  of  every  month 


goods  arrive. 


CARD  INDEXES 

She  enters  each  order  on  two  cards,  one  headed  with 
the  name  of  the  article  and  the  other  with  the  name 
of  the  firm.  Each  set  she  files  alphabetically  in  the 
proper  file. 


RECORDING  BUSINESS  TRANSACTIONS      33 


ARTICLE                                                  VALVES 

Date 

Firm 

Location 

Quantity 

Order  No. 

1921 

Jul.    16 
Aug.    4 
Nov.  16 

Barrett  and  Jones 
Delancey  Mfg.  Co. 
Barrett  and  Jones 

Cincinnati,  O. 
Denver,  Colo. 
Cincinnati,  O. 

12 
6 
10 

4386 
5234 

5837 

The  foregoing  card  shows  all  the  orders  given  for 
valves.  The  entry  of  the  order  number  enables  a 
person  to  turn  at  once  to  the  proper  place  in  the  order 
book,  if  details  are  desired. 

To  the  following  card  Miss  White  turns  to  obtain 
the  address  of  Bar- 
rett and  Jones,  from 
which  firm  she  has 
been  directed  to  or- 
der valves. 

On  this  card  she 
enters    the   number 


NAME    Barrett  and  Jones 

ADDRESS     1364  Water  St.,  Cincinnati,  O. 

BUSINESS    Plumbers'  Supplies 

SALESMAN    Aldcroft 

REMARKS    See  letter  of  VI-16-21 ;  prices 

ORDERS    4386,  5837 


of  the  order  last  sent,  then  files  it  away. 
INCOMING  BILLS 

When  the  two  invoices  (original  and  duplicate) 
reach  the  office  of  the  purchasing  agent,  Miss  White 
stamps  on  the  order  sheet  and  on  both  invoices  the 
date  they  are  received.  On  the  original  invoice  she 
also  stamps  a  form  to  be  initialed  by  the  proper  per- 
sons to  certify  (a)  that  the  specified  number  of  articles 
has  been  received;  (b)  that  each  is  of  the  proper 
quality;  (c)  that  the  prices  are  those  agreed  upon; 
and  (d)  that  the  extensions,  etc.,  are  correctly  made. 


34 


WALSH'S  BUSINESS  ARITHMETIC 


When  goods  arrive,  she  stamps  the  date  on  the  order, 
and  on  both  invoices,  and  sends  the  "original"  for 
certification  to  the  persons  passing,  respectively,  upon 
quality,  quantity,  and  price.  When  the  invoice  is 
returned  with  the  required  initials,  she  adds  hers  as 
to  the  correctness  of  the  extensions,  etc.,  and  passes  it 
along  to  the  company's  treasurer,  retaining  the  dupli- 
cate in  her  files. 

THE  INVOICE 

CINCINNATI,  O.,  Nov.  21,  1921 
BARRETT  AND  JONES 

Plumbers'  Supplies 
SOLD  TO  The  Harrison  Company 

Happy  Valley,  Ariz. 
Via  Freight  DATE  OF  ORDER  XI-1 6-1921  YOUR  No.  5837 


6 

2"  Brass  Valves,  F247                          7  .  50 

45  — 

Plus  5% 

2  25 

47 

25 

2 

3"  IBB  Valves,  F600                          15.00 

30  — 

Less  47  % 

15 

90 

2 

Victor  Gate  Valves                            22  .  50 

45  — 

Less  35% 

29 

25 

92 

40 

Bill  Received,  Nov.  24,  1921 

Goods  Received,  Nov.  27,  1921 

Quantities  Correct.  .  .  ^.  IS. 

Qualities  Correct.  .  /£  erf. 

Prices  Correct.^,  tt,.  &. 

Extensions  Correct.???.  W. 

WRITTEN  PROBLEMS 

1.  Copy  and  complete  the  following  invoice.  Try 
to  make  all  extensions  without  the  use  of  "side" 
calculations. 


RECORDING  BUSINESS  TRANSACTIONS       35 


Folio  649 
Terms:  Net  Cash 


Your  Order  8502 


BAILY  AND  MIDDLESEX 

Hotel  Sundries 

* 

Butte,  Mont.,  May  26,  1920 
SOLD  TO  Hotel  Burgundy 
Lorton  Valley,  Mont. 


<l> 

16 
17 

18 

19 
20 

100  doz.  Tea  Cups  #4982                1  .  05 
100             "     Saucers                        .78 
43             "     Dishes  6"  #4993       1.80 
19          Dishes  10"                         4.25 
5               "       12"                          7.09 
16          Celery  Trays                      4.40 
80          Tea  Cups  #4994                 1.05 
80          Saucers                                  .78 
30          Double  Egg  Cups             1.58 
141          Fruits  4"  #4995                     .72 
78              "       5"                              .90 
38          Bakers  3*                            1.58 
70          Plates  7"  #4996                  1  .  58 
40          Bakers  6"                            2.25 

105 

(a) 

5  Crates                           2.50 

12 

50 

(b) 

Write  extensions  in  the  first  double  column,  and 
the  footing  of  the  articles  at  (a)  in  the  second.  Write 
at  (6)  the  total  amount  due. 

2.  Make  out  a  bill  for  the  following  articles  for  a 
hotel: 

78  doz.  Towels 
10    "     Unbl.  Sheets  54  X  90 
12    "     Pillow  Cases  44  X  36 
50    "     Red  End  Towels 
25    "     Sheets  72  X  108 
256  yd.  Cheesecloth,  P.  red 


204  Pantry  Toweling 

200    "  Dish  P.  blue 

400    "  Glass  200  H 

408    "  Side  F.  white 

40^  "  Sheeting,  l%  Utica 

49    "  Fine  Glass  Toweling 


@  $4.50 
7.92 
1.74 
1.34 
11  — 
.06% 
.19% 
.19% 


.21 


36  WALSH'S  BUSINESS  ARITHMETIC 

THE  TIME   CLOCK 

Miss  White  ascertains  the  weekly  service  of  each  of 
the  12  employees  by  his  or  her  time  card. 

As  each  arrives  in  the  morning,  he  takes  his  card 
from  the  "OUT"  rack,  inserts  it  in  the  recording  in- 
strument in  the  time  clock,  and  pulls  a  lever.  By  doing 


this,  he  stamps  in  the  first  column  the  time  of  his 
arrival.  He  then  places  the  card  in  the  "  IN "  rack. 
When  he  leaves  at  noon,  he  takes  his  card  from  the 
"  IN  "  rack,  has  the  time  stamped  in  the  second  column, 
and  places  it  in  the  "OUT"  rack.  WTien  he  returns, 
he  replaces  the  card  in  the  "IN"  rack,  after  having 
had  the  time  recorded  in  the  third  column.  When  he 
leaves  for  the  day,  he  places  the  card  in  the  "OUT" 


RECORDING  BUSINESS  TRANSACTIONS      37 


rack,  after  the  time  has  been  recorded  in  the  fourth 
column,  or  in  the  sixth  column  in  the  case  of  "overtime." 

THE  TIME  CARD 

When  the  time  card  is  completed  by  the  insertion 
of  the  number  of  hours  of  daily  service,  the  weekly 
total,  the  amount  due,  and  the  employee's  receipt, 
it  presents  the  following  appearance: 

Number  4 

Name     D.  Marquard 


tco* 

.92 

A.M. 

Noon 

P.M. 

Overtime 

5    , 

C  i-i 

Hours 

ii 

In 

Out 

In 

Out 

In 

Out 

M. 

7.55 

12.05 

12.55 

5.00 

8 

Tu. 

7.57 

12.01 

1.03 

5.02 

73 

W. 

7.56 

12.08 

12.56 

5.00 

8 

Th. 

7.59 

12.02 

12.57 

5.01 

8 

F. 

8.00 

12.02 

12.58 

6.02 

9 

S. 

8.03 

1.02 

43 

Total 

452 

TIME  45^  HOURS.      RATE  $12 
Due  for  week  $12. 41 

I  hereby  acknowledge  receipt  in  full, 
(Signed)  DORA  MARQUARD 

These  employees  are  paid  a  weekly  rate  based 
upon  44  hours  of  service,  4  on  Saturday  and  8  on 
each  of  the  other  5  working  days.  When  oppor- 
tunity offers,  Miss  White  enters  in  the  last  column  the 
number  of  hours  of  service  rendered  each  day. 

Miss  Marquard,  not  having  been  late  or  absent  on 
Monday,  Wednesday,  or  Thursday,  Miss  White  enters 
the  number  of  hours  for  each  of  these  days  as  8.  She 


WALSH'S  BUSINESS  ARITHMETIC 


enters  7%  for  Tuesday,  owing  to  the  arrival  of  Miss 
Marquard  after  1.  She  makes  a  similar  deduction 
on  Saturday  after  allowing  the  overtime  of  an  hour. 
Friday's  entry  shows  9  hours,  which  includes  the 
overtime. 

On  Monday,  Miss  White  completes  the  time  cards, 
entering  Saturday's  time  on  each,  the  total  for  the 
week,  and  the  amount  due.  She  also  completes  the 
time  sheet,  shown  below,  having  made  as  many  of 
the  daily  entries  as  possible  in  her  spare  time  the 
preceding  week. 

As  a  check  on  the  accuracy  of  the  total  service 
entered  on  each  time  card,  and  the  amount  due,  she 
calculates  these  once  more  from  the  time  sheet,  and 
compares  the  results  with  those  shown  on  the  card. 

TIME   SHEET  —  WAREHOUSE 
Dec.  1,  1921  to  Dec.  6,  1921 


No. 

Name 

Mon. 

Tues. 

Wed. 

Thur. 

Fri. 

Sat. 

Hours 

Rate 

Pay 

1 

Cutshaw,  G. 

73 

8 

8 

72 

83 

4 

44 

15.— 

15.  _ 

2 

Daubert,  J. 

8 

73 

8 

82 

8 

4 

-441 

12.— 

12.07 

3 

Johnson,  J. 

72 

8 

8 

8 

9 

4 

442 

12.— 

12.14 

4 

Marquard,  R. 

8 

73 

8 

8 

9 

43 

452 

12.— 

12.41 

5 

Meyers,  J. 

7 

8 

8 

8 

78 

5 

433 

12.— 

11.93 

6 

Miller,  O. 

8 

8 

73 

8 

8 

4 

433 

11  

10.94 

7 

Mowery,  H. 

9 

8 

8 

73 

— 

— 

323 

10.50 

7.82 

8 

Olsen,  I. 

82 

8 

8 

8 

82 

4 

45 

10  

10.23 

0 

Pfeffer,  E. 

6 

— 

8 

8 

6 

43 

323 

9  

6.70 

10 

Rucker,  N. 

8 

8 

8 

— 

8 

4 

36 

8.50 

6.95 

11 

Stengle,  C. 

8* 

8 

8 

8 

9 

5 

462 

8.— 

8.45 

12 

Wheat,  Z. 

8 

8 

72 

8 

83 

4 

441 

6.— 

6.03 

Total 

94* 

87s 

951 

87» 

90» 

47* 

503 

120.67 

The  small  figures  above  the  others  and   to  the  right  denote  quarters; 
94l  meaning  94&  87*  meaning  87&  and  90s  meaning  90& 


RECORDING  BUSINESS  TRANSACTIONS      39 


CASH  FOR  THE  PAY  ENVELOPES 

After  verifying  the  correctness  of  the  total,  Miss 
White  prepares  a  check  for  the  amount.  This  she 
sends  with  the  time  sheet  to  the  purchasing  agent. 
When  the  latter  has  affixed  his  signature  to  the  check, 
he  sends  it  to  the  treasurer. 

THE  CHECK 


H-S 


11 

S    Q  & 


Happy  Valley,  Arizona,  Dec.  8,  1921  No.  8502 

THE  BATH  COUNTY  NATIONAL  BANK 

Pay  to  the  Order  of  Maurice  J.  Moore  $120%o 

One  Hundred  Twenty  %o Dollars 

Donald  Campbell 

Treasurer 


CHANGE  SLIP 
BATH  COUNTY  NATIONAL  BANK 


When  the  check  is  returned  to  Miss  White  with  the 
necessary  signatures  she  sends  Maurice  Moore  to  the 
bank  to  obtain  the  cash  for  the  pay  envelopes,  giving 
him  the  accompanying  "change  slip." 

After  Maurice  Moore's  arrival  at  the  bank,  he 
indorses  the  check 
and  presents  it  with 
the  "change  slip"  to 
the  paying  teller.  The 
latter  gives  him  the 
specified  bills  and  the 
smaller  change,  which 
he  counts.  Finding 
the  amount  correct, 
Maurice  returns  with 
the  money  to  Miss 
White.  She  distrib- 


Kindly  send   by  Maurice  Moore  the 
following: 

7$10's  $70.— 

6      5's  30.— 

5      2's  10.— 

5      1's  5.— 

5  halves  2.50 

6  quarters  1.50 
12  dimes  1.20 

5  nickels  .25 
22  pennies 

Total  $120.67 


40 


WALSH'S  BUSINESS  ARITHMETIC 


utes  it  in  the  pay  envelopes,  writing  on  the  back  of 
each  the  name  of  the  employee  and  the  amount  con- 
tained. Each  employee,  on  receiving  his  envelope  and 
counting  its  contents,  signs  the  receipt  on  the  time 
card.  When  all  the  employees  have  been  paid,  the 
cards  are  sent  to  the  auditor. 

To  determine  the  denomination  of  the  bills  and 
coins  needed  for  the  different  envelopes,  Miss  White 
makes  a  memorandum  in  the  following  form: 


CHANGE   MEMORANDUM 


No. 

Pay 

$10 

$5 

$2 

$1 

50£ 

25^ 

10* 

5i 

1* 

1 

15.— 

1 

1 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

2 

12.07 

- 

1 

- 

- 

_ 

- 

1 

2 

3 

12.14 

_ 

1 

- 

— 

- 

1 

- 

4 

4 

12.41 

- 

1 

- 

- 

1 

1 

1 

1 

5 

11.93 

- 

- 

1 

I 

1 

1 

1 

3 

6 

10.94 

- 

- 

- 

1 

1 

1 

1 

4 

7 

7.82 

_ 

1 

1 

_ 

1 

1 

_ 

1 

2 

8 

10.23 

1 

_ 

_ 

_ 

_ 

_ 

2 

_ 

3 

9 

6.70 

_ 

1 

_ 

1 

1 

_ 

2 

_ 

_ 

10 

6.95 

_ 

1 

_ 

1 

1 

1 

2 

_ 

_ 

11 

8.45 

_ 

1 

1 

1 

_ 

1 

2 

- 

_ 

12 

6.03 

- 

1 

- 

1 

- 

- 

- 

- 

3 

Tot. 

120.67 

7 

6 

5 

5 

5 

6 

12 

5 

22 

WRITTEN  EXERCISES 

Writing  in  a  column  the  amounts  due  the  different 
employees,  she  inserts  on  a  line  with  each  the  de- 
nominations required  for  the  envelope.  The  footings 
at  the  bottom  give  the  total  number  of  each  denomi- 
nation. This  she  verifies  when  she  makes  out  the 
change  slip. 


RECORDING  BUSINESS  TRANSACTIONS      41 

WAGE  TABLES 

To  insure  the  correctness  of  the  pay  rolls,  Miss 
White  obtains  the  results  by  two  different  methods: 
one  by  performing  the  calculations  in  the  common 
way,  and  the  other  by  the  use  of  the  wage  tables. 


PORTION   OF  WEEKLY  WAGE  TABLE 


Hrs. 

Rate  per  44-hour  week 

Hrs. 

44 

$15 

$12 

$11 

$10 

$9 

$8 

44 

X 

.0852 

.0682 

.0625 

.0568 

.0511 

.0455 

% 

% 

.1704 

.1364 

.125 

.1136 

.1023 

.0909 

% 

% 

.2557 

.2045 

.1875 

.1705 

.1534 

.1364 

% 

1 

.3409 

.2727 

.25 

.2273 

.2046 

.1818 

1 

2 

.6818 

.5455 

.50 

.4545 

.4091 

.3636 

2 

3 

1  .  0227 

.8182 

.75 

.6818 

.6136 

.5455 

3 

4 

1.3636 

1.0909 

1.— 

.9091 

.8182 

.7273 

4 

5 

1.7045 

1.3636 

1.25 

1.1364 

1.0228 

.9091 

5 

6 

2.0455 

1.6364 

1.50 

1.3636 

1.2273 

1.0909 

6 

7 

2.3864 

1.9091 

1.75 

1.5909 

1.4318 

1.2727 

7 

8 

2.7273 

2.1818 

2.— 

1.8182 

1.6364 

1.4545 

8 

9 

3.0682 

2.4545 

2.25 

2.0455 

1.8410 

1.6364 

9 

10« 

3.4091 

2.7272 

2.50 

2.2727 

2.0454 

1.8182 

10 

20* 

6.8182 

5.4545 

5.— 

4.5454 

4.0909 

3.6364 

20 

30 

10.2273 

8.1818 

7.50 

6.8182 

6.1364 

5.4545 

30 

40 

"18.6364 

10.9091 

10.— 

9.0909 

8.1818 

7.2727 

40 

50 

17.0454 

13.6364 

12.50 

11.3636 

10.2272 

9.0909 

50 

WRITTEN   EXERCISES 

1.  From  the  foregoing  table,  find  the  pay  at  the 
rate  of  $15  per  44-hour  week  for  (a)  36  hours,  (6)  27 
hours,  (c)  43%  hours,  and  (d)  39%  hours. 


42  WALSH'S  BUSINESS  ARITHMETIC 


METHOD 

(a)  30    hr.  $10.2273  (b)  20    hr. 

add_6      "      2.0455  add  _7      " 

36    hr.  27    hr. 

(c)  44    hr.  $15.  -  (d)  40    hr. 

less  _%__    «   less    %_    " 

43%  hr.  "  39%  hr. 

To  obtain  the  answer  to  (a),  take  from  the  $15 
column  of  the  table  the  amount  payable  for  30  hours, 
and  to  this  add  the  amount  for  6  hours. 


2.  Find  the  wages  payable  on  a  weekly  basis  of 
44  hours,  for  (a)  37  hours  at  $15,  for  (b)  42  hours  at 
$12,  for  (c)  37%  hours  at  $10,  for  (d)  49%  hours  at  $9, 
for  0)  54  hours  at  $8. 

3.  At  the  rate  of  $11  per  week  of  44  hours,  find  the 
amount  due  for  (a)  43%  hours,  for  (b)  28%  hours,  for 
(c)  39%  hours,  for  (d)  54%  hours. 


METHOD 

At  $11  for  44  hours,  the  hourly  rate  is  $%.  Multiply 
$X  by  (a)  43.5,  (b)  28.75,  etc.;  that  is,  the  quotient 
of  these  by  4  gives  the  wages  in  dollars. 


4.   At  the  specified  rates  for  44  hours,  find  the  wages 
due  for  services  rendered  as  follows: 

a  48  hours  at  $12  per  week         d  36  hours  at  $16  per  week 
b  40       "     "  $13    "      "  e  55       "       "$21      "       " 

c  52       "     "  $14    "      "  /  33       " 


RECORDING  BUSINESS  TRANSACTIONS      43 


5.  From  the  following  time  card  calculate  the  pay 
due  Miss  Jones  for  the  week,  deducting  %  hour  for 
an  absence  of  each  15  minutes,  or  less. 


NUMBER  14 

NAME    MARY  E.  JONES 

A.M. 

NOON 

P.M. 

Overtime 

Day 

Hours 

In 

Out 

In 

Out 

In 

Out 

M. 

7.56 

12.01 

12.55 

5.01 

Tu. 

8.03 

12.05 

1.02 

5.04 

W. 

7.59 

12.03 

12.59 

5.06 

5.30 

7.30 

Th. 

8.31 

12.02 

1.03 

6.01 

F. 

7.57 

12.04 

12.56 

5.03 

5.30 

6.30 

S. 

7.59 

12.03 

12.58 

2.31 

6.   From    the    following    pay    slip    determine    the 
hourly  rate  for  each  day: 

NAME  —  Marguerite  Carter 
OPERATION  —  Seaming  Coats 


Day 

Jan. 

Hr. 

Earnings 

Mon. 
Tues. 
Wed. 
Thurs. 
Fri. 
Sat. 

4 
5 

6 

7 
8 
9 

m 

8% 

$2.31 
2.25 
2.80 
2.45 
2.64 
1.36 

7.  Make  a  graph1  showing  the  fluctuations  during 
the  year  in  the  monthly  earnings  of  a  girl  employed 
in  a  "seasonal"  occupation: 

Jan.      $48  May     $27  Sep.      $44 

Feb. 


$48 
$50 
Mar.  $49 
Apr.  $35 


May 
Jun. 
Jul. 
Aug. 


$27 
$36 

$42 
$47 


Sep. 
Oct. 
Nov. 
Dec. 


1  For  a  description  of  graphs,  see  Section  III,  p.  123. 


CHAPTER  THREE 

SOME    BUSINESS    FORMS 

INVOICES   AND   BILLS 

WRITTEN  EXERCISES 

1.   Copy  and  complete  the  following  invoice: 


Akron,  Ohio,  Apr.  7,  1920 

CLARK,  STOWE,   &  CO. 

BUILDERS'  SUPPLIES 
SOLD  TO  Mr.  Albert  Janson. 


2450  Red  Brick  30.— 

85  bags  White  Sand  .30 

85  Sand  Bags  .06 

140  bdl.  Laths  4.85 


73  50 


6790 


In  a  bill  or  an  invoice  begin  with  a  small  letter  the  word 
denoting  the  quantity;  lb.,  bu.,  etc.  Begin  with  a  capital 
the  name  of  the  article.  Do  not  use  "of"  or  "@." 

Rule  your  paper  as  shown  above.  Write  each  extension 
in  the  first  double  money  column.  Write  the  footing  in  the 
second  double  money  column  on  the  line  below  the  last 
footing. 

2.  When  2450  bricks  cost  $73.50,   (a)  what  is  the 
price  of  one  brick?   (6)  How  many  can  be  bought  for  $30  ? 

3.  At  $4.85  per  thousand,  (a)  how  many  laths  can 
be  bought  for  $67.90?     (b)  If  this  quantity  is  contained 
in  140  bundles,  how  many  laths  are  there  to  a  bundle? 

44 


RECORDING  BUSINESS  TRANSACTIONS      45 

4.  When  52  bags  of  Portland  cement  cost  $30.55, 
(a)  what  is  the  cost  per  bag?  (6)  What  is  the  cost  of 
a  barrel  of  four  bags? 

6.  One  item  on  an  invoice  is  60  bags  of  K.  W. 
cement,  the  rate  per  unit  being  $12.50,  and  the  ex- 
tension $37.50.  (a)  How  many  pounds  are  there  in 
the  purchase  if  a  bag  contains  100  pounds?  (b)  How 
many  units  are  charged  for?  (c)  How  many  pounds 
are  there  in  the  unit?  (d)  What  is  the  unit? 

Invoice  clerks  do  not  write  "per  pound,'*  "per  gross," 
"per  ton,"  "per  thousand,"  etc.,  the  assumption  being  that 
the  buyer  knows  the  quantity  represented  by  the  given  rate. 


MADISON,  Wis.,  Apr.  30,  1920 
MR.  ALBERT  JANSON 

Bought  of  J.  P.  Duffy  Company 

Lime,  Lath,  Brick,  Cement,  etc. 
Terms,  Net  30  days. 


Apr. 

3 

1  cu.  yd.  Sand 

3 

_ 

5  bags  Port.  Cement                           2.35 

2 

94 

8 

4  bbl.  Marble  Dust                             1.75 

104  bags  Port.  Cement                       2.30 

12 

72     "        "                                           2.30 

13 

3  bbl.  N.  A.  Plaster                            1.95 

5 

85 

17 

12  bags  K.  W.  Cement                    12.50 

7 

50 

24     '•     Port.                                       2.40 

1  bbl.  Atlas 

5 

— 

21 

4500  Bricks                                        30.00 

150  bdl.  Laths                                    4.80 

4  bags  Atlas  Cem. 

5 

— 

(a) 

Or. 

27 

175  M.  T.  bags  Portland                     .08 

28 

72   "    "      "     K.  W.                          .06% 

3  "    "     "     R.  W.                          .06 

(6) 

Balance 

(<0 

46  WALSH'S  BUSINESS  ARITHMETIC 

In  the  last  invoice  the  given  price  of  brick  is  by  the  M; 
of  laths,  by  the  M,  each  bundle  containing  100  laths;  of 
Portland  cement,  a  barrel  of  four  bags;  of  K.  W.  cement, 
a  ton  of  2000  pounds,  each  bag  containing  100  pounds. 

6.  Complete  the  foregoing  invoice,  which  shows 
credits  for  empty  (M.  T.)  bags  returned.  It  differs 
from  a  statement  by  itemizing  the  purchases  made 
during  the  month. 

Write  the  total  debits  at  (a),  the  total  credits  at  (6), 
and  the  balance  at  (c). 

This  concern  renders  invoices  (bills)  once  a  month 
to  regular  customers.  When  the  goods  are  delivered, 
the  driver  obtains  a  receipt  in  the  accompanying  form, 
from  Mr.  Janson's  representative,  to  whom  he  gives 
a  carbon  duplicate. 

In  case  there  is  any  question  as  to  articles,  quanti- 
ties, etc.,  the  receipts  are 
referred  to. 

The  foregoing  invoices 
are  frequently  called  bills, 


MEMORANDUM 
RECEIVED  OP 

J.  P.  Duffy  Company 


1  cu.  yd.  Sand 
5  bags  Port.  Cem 


Signed . .  A.  Janson . 


per  M.  M.  W. 


Apr.  3,  1920.  -  T     • 

the  former  name  being 
more  particularly  applied 
to  the  next  form,  which 
designates  by  number  the 
case  in  which  each  item 
is  packed.  This  enables 
the  purchaser  to  locate  a  particular  article. 

The  goods  in  the  next  invoice  are  contained  in  two  cases;  one  marked 
A.  S.  53,  and  the  other  A.  S.  54.  Each  case  contains  6  pieces. 

7.  Complete  the  following  invoice.  Insert  at  (a)  the 
total  number  of  yards  in  the  second  three  pieces;  at 
(6)  the  total  in  the  next  six  pieces;  at  (c)  the  exten- 


RECORDING  BUSINESS  TRANSACTIONS      47 

sion  for  the  first  two  lots;  at  (d)  for  the  next  three;  etc. 

Place  the  footing  at  (g). 

SAN  FRANCISCO,  Aug.  27,  1919 

BUSSEY  &  TAYLOR 

Wholesale  Woolens 
SOLD  TO  Albert  Shields, 

Phoenix,  Arizona. 


A.  S. 

53 
54 

2  c/s  Woolen  Mantlings              53/54 
48%  yd. 
46%    '        94^yd.                           1.64 

C<0 

(d) 
(«) 

(/) 

(a) 

47%    " 
47%    " 
45%    "            (a)                             1.26 

61        "                                            2.25 

47K  yd. 
62%    " 
66%    " 
62^    " 
61       " 
48%    "            (&)                              1.26 

When  a  monthly  invoice  contains  a  great  number 
of  items,  several  are  placed  on  a  line  to  economize 
space,  as  in  the  following. 

KNOXVILLE,  TENN.,  Oct.  1,  1920. 
Mr.  Henry  Schlaefer 

Bought  of  Richard  H.  Wattles 
GRAIN,  HAY,  STRAW,  MILL  FEED 

Interest  charged  on  overdue  accounts 


Sep. 

1 

100#  Perfection  1.95;  1  bag,  .05 

2 

_ 

100#  Wh.  Bran,  1  .80;  100#  Middlings,  2.— 

3 

80 

1.09                                            97^ 

2  bu.  Corn,  2.18;  2bu.  Cr.  Corn,  1.95 

4 

13 

.05                                     .80 

2  bags,  .10;  2  bags  G.  A.  Salt,  1.60 

1 

70 

NOTE:  The  character  #  before  a  number  means  "Number";   after  a 
number,  it  indicates  "pounds." 


48  WALSH'S  BUSINESS  ARITHMETIC 

8.  Complete  the  foregoing  invoice  by  adding  the 
following:  Sep.  4,  2  bags  of  cracked  corn,  1  bag; 
Sep.  8,  100  pounds  Wheat  Bran,  600  pounds  of  corn 
bran,  2  bushels  of  corn,  7  bags;  Sep.  9,  100  pounds  of 
Perfection  feed,  1  bag;  Sep.  10,  2  bushels  of  cracked 
corn,  1  bag;  Sep.  11,  200  pounds  of  wheat  bran,  100 
pounds  of  middlings,  400  pounds  of  beet  pulp,  400 
pounds  of  corn  bran,  4  bushels  of  corn,  2  bushels  of 
middlings,  7  bags;  Sep.  16,  100  pounds  of  Perfection 
feed,  2  bushels  of  cracked  corn,  2  bags;  Sep.  17,  200 
pounds  of  wheat  bran,  £00  pounds  of  cotton  seed 
meal,  200  pounds  of  beet  pulp,  200  pounds  of  gluten, 
100  pounds  of  middlings,  4  bushels  of  corn,  2  bags; 
Sep.  22,  500  pounds  of  gluten,  200  pounds  of  wheat 
bran,  200  pounds  of  beet  pulp,  200  pounds  of  corn 
bran,  2  bushels  of  corn,  2  bushels  of  cracked  corn, 
1  bag;  G.  A.  salt,  4  bags;  Sep.  28,  200  pounds  of 
cotton  seed  meal,  200  pounds  of  wheat  bran,  200 
pounds  of  gluten,  400  pounds  of  corn  bran,  100  pounds 
of  middlings,  2  bushels  of  corn,  2  bushels  of  cracked 
corn,  6  bags. 

Use  the  following  prices : 

Cracked  corn,  $  .97%  per  bu.  Middlings,  $2.00  per  100  Ib. 

Corn,  $1.09     "    "  Beet  pulp,  $1.35  "     "     " 

\\hoatbran      $1.80     "    100  Ib.  Cottonseed  meal,  $1.85  per 
Corn                  $1.30    per  100  Ib.        100  Ib. 

Perfection  feed  $1.95     "    100"  Gluten,       $1.85  per  100  Ib. 

Bags,  5  cents  each  G.  A.  salt,  $  .80  per  bag 

While  every  invoice  may  be  called  a  bill,  bills  con- 
taining items  for  services  rendered  are  not  invoices. 


RECORDING  BUSINESS  TRANSACTIONS      49 

In  bills  of  this  kind  the  heading  "Bought  of"  or  "Sold 
to"  is  changed  to  the  form  given  in  the  following 

BILL  FOR  SERVICES  AND   MATERIALS 

TOPEKA,  KAN.,  Jun.  11,  1920 
Mr.  Robert,  P.  Webb 

85th  Street  and  Ridge  Boulevard 

To  JOHN  TODD,  Dr. 

Plumbing  Contractor 


1  Range  $268 

48 

_ 

2      "      Couplings,  %"                     .37# 

1  Nippb,  %' 

10 

10#  Galv.  Fittings                             .  15 

3  Unions                                             .37 

19  ft.  2  in.  Pipe                                 .12 
1  Boiler  Coupling 

60 

2  Couplings,  water  back                  .  62)£ 

10  Nipples                                          .13 

2  Els,  %"                                            .  15 

1  Tee,  1" 

15 

2  Elbows,  45  degrees                        .  15 

3  lengths  Pipe                                    .  10 

1  Damper,  6* 

30 

2  Black  Elbows,  6"                           .20 

1  Brass  Ring 

9 

— 

1  Galv.  Cross 

20 

2     "      Ells                                        .15 

4      "      Elbows                                  .10 

2  Black  Ells                                      .15 

1  Plate  Rack 

3 

— 

Time,  2M  days                                4.— 

Received  Payment 
June  15,  1920 

JOHN  TODD 

per  W.  H.  M. 

9.  Copy  and  complete  the  foregoing  bill. 

10.  Make  out  a  check  on  the  School  Bank  in  settle- 
ment of  the  foregoing  bill. 


50  WALSH'S  BUSINESS  ARITHMETIC 

RECEIPTS 

A  person  to  whom  an  express  package  is  delivered, 
a  telegram,  a  special  delivery  letter,  etc.,  acknowl- 
edges the  delivery  by  writing  his  name  in  the  proper 
place  in  the  receipt  book  carried  by  the  messenger, 
driver,  carrier,  etc. 

The  receipt  of  Mr.  Brown's  money  by  a  bank,  on 
deposit,  is  shown  by  the  teller's  entry  in  the  passbook. 
When  Mr.  Webb  settled  Mr.  Todd's  bill,  the  latter 
indicated  the  fact  by  "receipting"  the  bill.  If  Mr. 
Webb  did  not  have  the  bill  with  him,  Mr.  Todd's 
clerk  would  give  him  the  following 

RECEIPT   IN   FULL 


TOPEKA,  KAN.,  Jun.  15,  1920. 

RECEIVED  OF  MR Robert  P.  Webb 

Too  DOLLARS 

in  full  of  account  to  date. 

JOHN  TODD 
$ per 


11.  Copy  and  complete  the  foregoing  receipt,  in- 
serting the  dollars  in  words  on  the  third  line,  and  in 
figures  on  the  last  line,  expressing  the  cents  as  a  frac- 
tion of  a  dollar  in  each  place.     Use  your  own  initials 
as  the  clerk  who  receives  the  money  for  Mr.  Todd. 

12.  Write  John  Whalen's  receipt  for  $125,  sent  him 
by  Hiram  Hunt  for  the  rent  of  his  store  for  Jun.,  1920. 
Insert  on  the  third  line  "For  rent  of  premises  No.  4 
Court  Square  for  June,  1920." 


RECORDING  BUSINESS  TRANSACTIONS      51 

CHECKS  AS  RECEIPTS 

To  save  the  time  and  expense  of  mailing  receipted 
bills  to  thousands  of  customers  making  monthly 
settlements  by  check,  many  business  concerns  print 
at  one  end  of  the  bill  a  coupon  to  be  detached  therefrom 
and  inclosed  with  the  check  sent  in  payment,  unless 
the  customer  prefers  to  send  the  bill,  and  to  have  it 
returned  to  him  receipted. 


If  no  further  receipt  is  desired,  detach  this  coupon  and 
mail  with  your  check. 
The  canceled  check  is  your  receipt. 
Date,  Jul,  31,  1920  W.  S.  Julius  &  Co. 

Mrs.  J.  Carroll  Payne,  Folio  35814 

8502  Hamilton  Boulevard.          Amt.  $114 . 42 


Some  bills  contain  a  form  similar  to  the  one  on  the 
right  in  which  the  customer  CUSTOMER'S  RECORD 

makes  the  necessary  entries.  Paid  by  Check  No.  V- 7 6 

If  a  second  bill  for  the  same  Bank  ^^^  i/tA*ol 

purchases     should    be    pre-  Date>  ^'  *'  f^° 

sented,  the  record  on  the  original  bill  will  furnish  the 
number  of  the  check.  The  presentation  of  the  can- 
celed check  with  its  indorsement  showing  that  it  was 
collected  by  the  merchant  will  be  satisfactory  evidence 
that  the  bill  was  paid,  and  that  he  made  an  error  in 
rendering  the  second  bill. 

It  is  unnecessary  to  state  that  receipts,  receipted 
bills,  and  canceled  checks  should  be  carefully  preserved. 

13.  Copy  and  complete  the  following  check  by  which 
Mrs.  Payne  pays  the  bill  of  A.  D.  Winkle  for  $84.75. 
She  notes  in  the  left  the  purpose  of  the  check  and 


WALSH'S  BUSINESS  ARITHMETIC 


signs  the  check  with  her  own  name.  She  also  notes 
upon  her  check-book  stub  the  purpose  of  the  check,  and 
mails  it,  with  the  coupon.  She  fills  out  the  "  Customer's 
Record"  on  the  bill  and  files  away  the  latter. 


§1 

TUCSON,  ARIZ.,  Aug.  3,  1920 

No.  476 

o 

ARIZONA 

SCHOOL  BANK 

g« 

S>1 

Pay  to  the 

U       - 

$  

~  >-» 

Dollars. 

c  3s 

Elizabeth  Payne.. 

ORDERS  FOR  GOODS 


When  a  merchant  orders  goods  by 


ORDER  SLIP 

Fairfax  Furniture  Co. 

Brockton,  N.  Y. 

Dressers  and  Chiffoniers 

VI-9-1920 

Salesman 

Yates.     Order  No.  231 

Ship  to  Jervis  Johnson  &  Co. 

Address  —  255  Columbia  Ave.,  Passaic,  N 

J. 

Ship  via  Penn.  R.  R.     Terms  —  60;  5/30 

F.  o.  b.  Brockton. 

Quantity 

No. 

Finish 

Price 

3 

2784 

Mah.  Dress 

11 

75 

3 

2658 

"     Chiff. 

12 

50 

3 

3062 

Oak  Dress. 

12 

25 

S 

3817 

"    Chiff. 

12 

75 

J.  JOHNSON  &  Co. 

mail  he  retains 
a  carbon  copy  of 
the  order  slip  in 
the  order  book 
(see  p.  32).  When 
he  gives  a  verbal 
order  to  a  seller's 
agent,  the  latter 
makes  out  a  slip. 
In  the  accom- 
panying one  Mr. 
Yates,  a  sales- 
man .  for  the 
Fairfax  Furni- 
ture Company, 
sells  Jervis  John- 
son &  Co.  the 
specified  articles 
at  the  prices 


RECORDING  BUSINESS  TRANSACTIONS      53 

given.  The  slip  shows  the  terms  of  credit  and  that 
the  goods  are  to  be  delivered  to  the  railroad  company. 

Mr.  Yates  obtains  the  signature  of  J.  Johnson  & 
Co.  to  the  original,  which  he  sends  to  the  Fairfax 
Furniture  Co.  He  gives  a  carbon  duplicate  to  J. 
Johnson  &  Co.  for  their  files. 

The  following  is  the  invoice: 


No.  647 


Fairfax  Furniture  Company 
Manufacturers  of  Dressers  &  Chiffoniers 


Order  No.  231.     Dated  VI-9-1920. 
Sold  to  Jervis  Johnson  &  Co. 

255  Columbia  Ave.,  Passaic,  N.  J. 

Shipped  by  Penn.  R.  R.     Car  P.  R.  R.  85026 
F.  o.  b.  —  R.  R.    Terms:  60  da.  net;  5  %,  30  da. 


Brockton,  N.  Y.,  June  11,  1920 
Salesman  Yates. 


3  Mah.  Dress.        11.75 
3      "      Chiff.         12.50 
3  Oak  Dress.          12.25 
3    "    Chiff.           12.75 

NOTE;   F.o.b.  —  R.  R.  means  that  the  goods  are  delivered  to  the  rail- 
road company  without  charge  for  cartage  —  "Free  on  Board." 

WRITTEN  EXERCISES 

1.  Copy  and  complete  the  foregoing  invoice. 

2.  Make  out  a  check  on  the  Passaic  National  Bank 
for  the  amount  of  the  bill,  dating  the  check  about 
40  days  after  Jun.  11. 

3.  Make  out  a  check  to  the  order  of  the  Pennsyl- 
vania   Railroad    Company    for    the    freight   on    2700 
pounds  at  45  cents  per  100  pounds. 


54 


WALSH'S  BUSINESS  ARITHMETIC 


BILL   OF  LADING 

When  the  goods  are  delivered  to  the  railroad,  the 
freight  agent  gives  the  shippers  a  Bill  of  Lading, 
which  is  a  form  of  receipt,  acknowledging  that  the 
goods  have  been  delivered  to  the  railroad.  The 
Fairfax  Company  mails  this  bill  of  lading  to  Jervis 
Johnson  &  Co.,  who  present  it  to  the  freight  agent 
at  Passaic  as  evidence  that  they  are  the  owners. 

The  following  is  an  abbreviated  form  of  a 

BILL  OF  LADING 

Pennsylvania  Railroad  Company 

Date    Jun.  11,  1920 

Received  at  Brockton,  N.  Y.,  from  Fairfax  Furniture  Co. 

the  property  described  below,  in  apparent  good   order 

except  as  noted,  contents  and  condition  of  contents  of 

package  unknown. 

The  rate  on  freight  from  Brockton,  N.  Y.,  to  Passaic,  N.  J.  is  in 

cents  per  100  pounds 


1st  class 

2d  class 

3d  class 

4th  class 

5th  class 

6th  class 

Special 

45 

Consigned  to  Jervis  Johnson  &  Co.,  255  Columbia  Av. 

Destination,  Passaic,  State  of  New  Jersey 

Route  N.  Y.  C.,  Penn.        Car  Initial  P.  R.  R.     Car  No.  85026 


Number  of 
Package 

Description 

Weight 

6 
6 

Crates  Dressers 
Chiffoniers 

750  # 
600  # 

ANDREW  JAV1NS,  Agent 
per  M.  E.  K. 


RECORDING  BUSINESS  TRANSACTIONS      55 


Upon  presentation  of  the  bill  of  lading  and  the 
payment  of  the  freight  the  twelve  crates  are  delivered 
to  the  consignees. 


FREIGHT  BILL 


Consignees:  Jervis  Johnson  &  Co.  No.  1669 

255  Columbia  Av.  Date  VI-16-1920 

To  Pennsylvania  Railroad  Company,  Dr. 

Passaic  Station,  from  Brockton,  N.  Y. 
Waybill  No.  92    Date  VI-1 1-1919 
Via  N.  Y.  C.,  Penn.         Car  P.  R.  R.  85206 


FREIGHT 
BILL 


Shipper 

Fairfax  Furniture  Co. 


Original  Point  of  Shipment 

Brockton,  N.  Y. 


Description  of  Articles 

Weight 

Rate 

Charges 

Total 

6  crt.  Dressers 
6    "    Chiffoniers 

1500 
1200 

45 

2700 

Claims  for  loss  or  damage  must  be 
promptly  made  in  writing  to  Freight 
Agent  accompanied  by  this  bill. 

Make  check  payable  to 
Pennsylvania  Railroad  Company 


Received  Payment  for  the  Company 

Jun.  16,  1920 
John  Carrol 

Freight  Agent 


WRITTEN  EXERCISES 

1.  Find  the  amount  of  the  foregoing  freight  bill. 

2.  Make  out  a  bill  for  the  following  articles  bought 
of  the  Wolverine  Manufacturing  Company  of  Detroit, 
Mich.:    4  mahogany  library  tables,   at  $9.65;    4   at 
$7.75,  4  at  $8.75;   8  golden  oak  parlor  tables  at  $1.50; 
and  8  mahogany  parlor  tables  at  $1.55. 


56  WALSH'S  BUSINESS  ARITHMETIC 

Insert  catalogue  numbers  to  denote  the  styles. 
Use  Mah.  for  mahogany,  G.  O.  for  golden  oak,  Lib. 
for  library,  Par.  for  parlor,  Tab.  for  table. 

3.  Make  out  a  freight  bill  for  the  delivery  of  the 
foregoing  goods  in  the  home  town.     Obtain  from  the 
local  freight  agent  the  rate  on  furniture  from  Detroit, 
also  a  copy  of  a  bill  of  lading  and  a  blank  freight  bill. 

Assume  that  the  articles  are  shipped  hi  28  boxes; 
the  legs  in  8  boxes  weighing,  with  the  contents,  15 
pounds  each;  each  library  table  top  in  a  box,  weighing 
with  its  contents  70  pounds;  the  16  parlor  table  tops 
in  8  boxes,  each  weighing  with  its  contents  85  pounds. 

4.  Make  out  an  order  slip  for  the  forgoing  articles, 
using  the  form  shown  on  p.  52.     Insert  the  catalogue 
numbers,  but  not  the  prices. 

5.  Make  out  a  check  on  the  School  Bank  for  the 
amount  of  the  bill. 

Be  careful  in  your  selection  of  dates  to  allow  a 
proper  interval  to  elapse  between  the  date  of  the 
order,  that  of  the  bill,  and  that  of  the  freight  bill. 

For  other  business  forms  see  Statements,  Notes,  Drafts,  Bills  of  Ex- 
change, Trade  Acceptances,  etc. 


SECTION  II 

BUSINESS  CALCULATIONS 

CHAPTER  ONE 

PERCENTAGE 

PREPARATORY  EXERCISES 

1.  A  sales  girl  received,  as  part  of  her  pay  $6  on 
sales  of  $120.     (a)  What  fraction  of  the  amount  of 
her  sales  did  she  receive  in  this  way?     How  much 
should  she  receive,  at  the  same  rate,  on  sales  (6)  of 
$150?     (c)  Of  $100? 

2.  A  man  received  $9  on  sales  of  $150.     (a)  What 
fraction  of  the  amount  of  his  sales  did  he  receive? 
How  much  should  he  receive  on  sales  (6)  of  $200? 
(c)  Of  $100? 

3.  (a)  How  many  problems  out  of  20  should  a  boy 
solve  who  solves  95  out  of  100?     (b)   How  many  out 
of  25  should  a  girl  solve  who  solves  96  hundredths  of 
her  problems? 

A  rate  of  $6  on  $100  is  stated  in  business  as  6  per 
cent,  which  means  6  hundredths,  or  .06.  It  is  written 
6%. 

Any  decimal  may  be  written  as  a  per  cent  by  express- 
ing it  in  hundredths,  omitting  the  decimal  point, 
and  placing  after  it  the  per  cent  sign.  Thus  5  tenths, 
which  is  equal  to  50  hundredths,  is  written  50%; 
125  thousandths,  which  is  equal  to  12%  hundredths, 

57 


58  WALSH'S  BUSINESS  ARITHMETIC 

is  written  12%%;    36  thousandths,  which  is  equal  to 
3.6  hundredths,  is  written  3.6  %. 


FINDING  THE  PERCENTAGE 
WRITTEN  EXERCISES 

1.  (a)  How  much  does  a  man  receive  who  is  given 
6%  of  $347.50?  (6)  How  much  weight  is  lost  during 
the  whiter  by  256  tons  of  hay,  if  the  loss  in  weight  is 
3%?  (c)  What  is  the  cost  of  insuring  a  store  for 
$7500  when  the  rate  is  %  of  1  %?  (d)  How  many 
pounds  of  butter  fat  are  there  in  231  pounds  of  milk, 
when  it  contains  3.6  %  of  butter  fat? 


METHOD 

Base           (a)  $347.50 
Rate                   X    .06 

(6)  256  T. 
X.03 

(c)  $7500 
X  .00% 

Percentage     $20.8500  Ans. 

7.68  T. 

$37.50 

To  find  the  percentage,  multiply  the  base  by  the 
rate  expressed  as  a  decimal. 

2.  A  salesman  receives  a  commission  of  3%  on  the 
amount  of  his  sales.     How  much  does  he  receive  on 
sales  of  $1575? 

3.  A  man  bought  a  house  for  $3500  and  sold  it  at 
a  profit  of  35  %.     (a)  What  was  his  profit?     (b)  How 
much  did  he  receive  for  the  house? 

4.  In  a  school  of  425  pupils  96  %  of  them  are  present, 
(a)  How  many  are  present?     (6)  What  per  cent  are 
absent?     (c)  How  many  are  absent? 


BUSINESS  CALCULATIONS  59 

5.  In  this  school  48  %  of  the  pupils  are  boys,    (a)  How 
many  boys  are  in  the  school?     (6)  how  many  girls? 

6.  How  many  hits  does  a  player  make  in  480  at- 
tempts, when  35%  of  his  attempts  are  successful? 

7.  How  much  tax  does  an  owner  pay  when  he  pays 
%%  of  $7800  which  is  the  valuation  of  his  farm  for 
purposes  of  taxation? 

8.  A  contractor   agrees  to  do  a  piece  of  work  in 
140  days.     How  many  days   should  he  require  to  do 
65  %  of  the  work? 

9.  A  dealer  bought  a  suit  of  clothes  for  $15  and  sold 
it    at    an    advance    of    66%%.      (a)  How   much   was 
the  advance?     (b)  The  selling  price?     It  takes  30% 
of  the  selling  price  to  do  business.      (c)   What  did 
it  cost  him  to  sell  the  suit?     (d)  What  was  his  net 
profit? 

10.  A  man  whose  income  is  $1500  a  year,  spends 
24  %  of  it  for  rent.     How  much  is  his  rent  (a)  for  a 
year?     (b)  For  a  month? 

SIGHT  EXERCISES 

1.  Change  to  common  fractions,  lowest  terms: 

a  .4          b  .14  c  .124  d  .3125 

e  .8  /  .32  g  .328  h  .5625 

2.  Express  as  per  cents : 

ay,     by,      c  y4      dy,      e  %     f  % 
g  %     kylQ     i  %      j  %      k%      l  % 

m  %       n%5       o%)       P%»       9  %        r  % 
s  t  %        us/lQ       v  %o       w  V*       x%Q 


60  WALSH'S  BUSINESS  ARITHMETIC 

3.  Express  as  common  fractions,  lowest  terms 

a  25%  650%  c  33%%          d87%% 

i  37%  %    j  83%  %    k  62%  %    /  8%  % 

4.  Find  (a)  25  %  of  36,  (b)  6%  %  of  75 


METHOD 

(a)  25  %  of  36  =  %  of  36  =  9,  Ans. 

(&)  6%%  of  75  =  %5  of  75  =  5,  Ans. 
Change  per  cents  to  fractions. 


5.   Give  answers: 


a  25  %  of  96 
d  6%  %  of  176 
g  37%%  of  480 
j  87%%  of  88 

b  33%%  of  69 
e  75  %  of  72 
*  8%  %  of  252 
A;  62%%  of  840 

c  12%%  of  248 
f  66%%  of  99 
i  50  %  of  83 
1  6%  %  of  165. 

6.   Find  (a)  4%  of  375;   (b)  6%  of  450. 


ONE   WAY 

(a)  4%  of  375  =  .04X375  =4X3.75  =4X3%  =  15,   Ans. 

(6)  6%  of  450  =  .06X450  =  6X4.5  =  6x4%=27,  Ans. 
Instead  of  taking  the  rate  in  hundredths,  divide  the 
base  by  100,  changing  the  quotient  to  a  mixed  number. 


7.   Give  answers: 

a  4  %  of  975         b  12  %  of  633%  c  8  %  of  937% 

d  6  %  of  850         e  16  %  of  412%  /  6  %  of  566% 

g  8  %  of  725         h  24  %  of  216%  i  9  %  of  833% 


BUSINESS  CALCULATIONS  61 

8.  Find  (a)  69%  of  33%;   (6)  88%  of  37%. 


METHOD 

(a)  69  %  of  33%  =  33%  %  of  69  =  %  of  69  =  23,  Ans. 
(6)  88  %  of  37%  =  37%  %  of  88  =  %  of  88  =  33,  Ans. 


9.   Give  answers: 

a  99  %  of  33%  b  88  %  of  25  c  72  %  of  16% 

d  48  %  of  12%  «  84  %  of  75  /  66  %  of  66% 

0  32  %  of  37%  A  92  %  of  50  i  56  %  of  62% 


WRITTEN  EXERCISES 

1.   A   merchant's    sales   were   $14,880   last   month. 
How  much  will  be  this  month's  increase  at  the  rate 

(a)  Of  25%?    (b)  Of  33%%?    (c)  Of 


METHOD 

(a)  $14,880          (b)  $14,880  (c)  $14,880 

X25  .33%  .06% 

$3,720  Ans.  $4,960  Ans.  $930  Ans. 

Write  the  given  per  cents  as  shown  above,  but 
obtain  the  result  by  dividing  $14,880,  the  base, 
by  4  in  (a),  by  3  in  (6),  by  16  in  (c):  that  is, 
multiply  the  base  by  %,  %,  and  %6,  the  fractional 
equivalents  of  the  respective  rates. 


2.   Write  answers  from  the  book: 

a  25  %  of  24,672         6  33%  %  of  34,569         c  6%  %  of  17,632 
d  50  %  of  17,976         e  11%  %  of  96,543         /  8%  %  of  12,396 


62  WALSH'S  BUSINESS  ARITHMETIC 

METHOD  BY  ALIQUOT   PARTS 

While  at  school  a  pupil  should  accustom  himself  to 
the  employment  of  methods  used  in  the  business  world, 
specimens  of  which  are  given  in  the  following  examples : 

3.  Find  (a)  37%%  of  872,  (b)  62%%  of  984,  (c)  27%% 
of  548,  (d)  36%%  of  936. 


METHOD 

(a)  37%%  of  872  (b)   62%%  of  984 

25%  =  218          50%  =  492 

+  12%%  =  109  +  12%%  =  123 

37%%  =  327  Ans.  62%%  =  615  Ans. 

(c)     27%%  of  548  (d)     36%  %  of  936 
25%  =  137  33%%  =  312 

+    2%%  =    13.7  +    3%%  =     31.2 

27%%  =  150.7  Ans.  36^%  =  343.2  Ans. 

In  (a)  find  25  %  of  872  by  taking  }{ of  it;  find  12%  % 
of  872  by  taking  %  of  the  one-fourth.  Test  (a) 
by  multiplying  109  by  3;  (6)  by  multiplying  123 
by  5;  (c)  by  multiplying  13.7  by  11;  (d)  by  multi- 
plying 31.2  by  11.  Why? 


4.   Find  answers: 

a  37^  %  of  392  b  62%  %  of  664  c  27%  %  of  680 
d  36%  %  of  780  e  31^  %  of  384  /  56#  %  of  7G8 
g  5&A  %  of  760  //  :*6%  %  of  690  i  18%  %  of  5*4 

6.   Find  (a)  17X%,    (6)  68«%,  (c)  81H%,  (<Z)  43%%, 
respectively,  of  1760. 

In  (a),  take  12%  %,  5  %  and  2%  % 
In  (6),  take  50%,  12%%  and 


BUSINESS    CALCULATIONS  63 

6.  Find  answers: 

a  17%  %  of  564       b   68%  %  of  932       c   81#  %  of  676 
d  43%  %  of  896       e    18%  %  of  736       /  37%  %  of  684 

7.  Find  (a)  18%%  of  972,  (b)  67%%  of  784,  (c)  38%% 
of  496. 

In  (a)  take  10  %,  5  %,  and  3%  %  (%  of  10  %) 
In  (6)  take  50  %,  12/2  %,  and  5  %  (Ko  of  50  %) 
In  (c)  take  25  %,  12%  %  and  1  % 

8.  Find  answers: 

a    13%%  of  864       6   17%%  of  396       c  122%%  of  444 
d    34%  %  of  675       e   18%  %  of  555      /  67%  %  of  712 

9.  There  are  five  schools  in  a  district.     The  largest 
has  a  register  of   1296  pupils.     The  registers  of  the 
others   are    (a)    75%,    (6)    66%%,    (c)    87%%,   and    (d) 
83%%,  respectively,  of  the  foregoing.     Find  the  regis- 
ter of  each. 

Find  %,  %,  %,  and  %,  respectively,  of  1296  by  deducting 
from  the  latter  %,  %,  %,  and  %,  respectively,  of  itself. 

10.  Find  answers : 

a  75  %  of  976       b  66%  %  of  687       c  87%  %  of  672 
d  83%  %  of  876     e  75  %  of  872         /  66%  %  of  876 

FINDING  THE  RATE 
PREPARATORY  EXERCISES 

1.  When  a  ball  player  makes  100  hits  in  300  at- 
tempts, (a)  what  fraction  of  his  attempts  are  succes- 
ful?     (6)  What  per  cent? 

2.  When  a  girl  has  worked  19  examples  out  of  20 
(a)    what  fraction   of   her   work  has   she  completed? 
(6)  What  decimal?     (c)  What  per  cent? 

3.  A  man  pays  27  dollars  taxes  on  property  valued 
at  36  hundred  dollars,     (a)  What  fraction  of  a  dollar 


64  WALSH'S  BUSINESS  ARITHMETIC 

does  he  pay  on  each  $100  of  valuation?     (b)  What  is 
the  rate  per  cent? 

4.  A  dealer  sold  at  a  profit  of  $160  an  article  that 
cost  him  $400.     (a)  What  fraction  of  the  cost  was  the 
profit?     (6)  What  decimal?     (c)  What  per  cent? 

5.  50   is   what   fraction    (a)  of    150?      (6)  Of  300? 
(c)  Of  250?     (d)  Of  75?     (e)  Of  60? 

6.  150    is    what    (improper)    fraction    (a)    of    100? 
(6)  Of  90?     (c)  Of  60?     (d)  Of  125? 

SIGHT  EXERCISES 

1.  What  is  the  rate  of  profit  (a)  on  suits  costing  $15 
each  and  sold  at  a  profit  of  $10  each?  (b)  On  land 
costing  $60  per  acre,  and  sold  at  a  profit  of  $75  per 
acre? 


METHOD 

(a)  10/i5  =  %  =  66%%,  Ans.    (b)  75/6o  =  %  =  125  %,  Ans. 
Divide  the  profit  (percentage)  by  the  cost  (base). 
Express  the  fractional  (or  decimal)  result  as  a  per 
cent. 


2.   Give  rates  per  cent: 

a  What  per  cent  of  36  is  18?  b  36  is  what  per  cent  of  18? 

c  23  is  what  per  cent  of  69?  d  What  per  cent  of  23  is  69? 

e  What  per  cent  of  32  is  24?  /  32  is  what  per  cent  of  24? 

g  99  is  what  per  cent  of  66?  h  What  per  cent  of  99  is  66? 

i  What  per  cent  of  80  is  30?  j  80  is  what  per  cent  of  30? 

WRITTEN  EXERCISES 

1.  (a)  What  is  a  dealer's  profit  when  he  gains  15%  % 
of  his  investment  of  $16,000?  (b)  What  is  his  rate  of 
profit  when  he  gains  $2480  on  an  investment  of  $16,000? 


BUSINESS  CALCULATIONS  65 


METHOD 

(a)  $16000  (b)  16000)2.480 

/15%  .15% 

$2480  Ans.  15%%  Ans. 

In  (a)  cancel  the  decimal  point  in  one  factor  and 
two  ciphers  in  the  other.  Use  160  as  the  multiplier 
(seep.  307). 

In  (6)  divide  $2480,  the  percentage,  by  $16,000, 
the  base.  Reject  the  dollar  signs,  cancel  the  three 
ciphers  in  the  divisor  and  set  off  three  decimal 
places  in  the  dividend  (see  p.  309).  Change  15% 
hundredths  (.15%),  the  quotient,  to  15%  per  cent 
05%%). 


In  (a)  are  given  the  base,  $16,000,  and  the  rate, 
15%%,  from  which  the  percentage  is  to  be  found. 
In  (b)  are  given  the  base,  $16,000,  and  the  per- 
centage, $2480,  from  which  the  rate  is  to  be  found, 
(a)  may  be  expressed  thus :  (b)  may  be  expressed  thus : 
15%%  of  $16,000  =  ?  ?  %  of  16,000  =  2480 

To  find  how  many  times  16,000  equals  2480,  find 
the  number  of  times  the  former  is  contained  in  the 
latter. 


To  find  the  RATE,  divide  the  PERCENTAGE  by  the  BASE. 
Express  the  quotient  as  hundredths,  and  replace  the 
decimal  point  by  the  per  cent  sign. 


2.   A   salesman   received   $94   commission   on   sales 
of  $3760.     What  was  the  rate? 


66  WALSH'S  BUSINESS  ARITHMETIC 

3.  A  man  received  $26.40  yearly  interest  on  a  loan 
of  $4800.     What  was  the  rate? 

4.  In  a  year,  the  population  of  a  village  increased 
from  720  to  768.     What  was  (a)  the  increase  for  the 
year?  (b)  The  rate  per  cent  of  increase? 

5.  Wliat  was  (a)  the  decrease  when  the  population 
fell  off  in  a  year  from  768  to  720?    (b)  The  rate  per 
cent  of  decrease? 

6.  (a)  What  %  of  496  is  217?    (b)  527  is  what  %  of 
465? 


METHOD 

.4375  1.13% 

(a)  496)217.0  (6)  465}527T 

1860  620 

3720  1550 

248  155 


Ans.  113%%,  Ans. 

Test  by  finding  (a)  43%%  of  496,  (b)  113%%  of  465 

NOTE.     For  this  form  of  division,  see  p.  307. 


The  foregoing  tests  show  merely  that  the  division 
has  been  correctly  made;  they  do  not  determine  that 
the  proper  number  has  been  taken  as  the  base  (the 
divisor). 

The  latter  is  more  clearly  indicated  to  some  pupils 
when  they  state  the  problem  in  the  form  of  an  equation 
as, 

(a)  ?  %  of  496  =  217;  ?  %  X  496  =  217 

(b)  527  =  ?  %  of  465;          527  =  ?  X  465 


BUSINESS  CALCULATIONS  67 

This  shows  them  that  in  (a)  217  is  the  percentage 
and  that  in  (b)  the  percentage  is  527,  the  base  in  each 
being  the  number  following  the  word  "of,"  which  may 
be  replaced  by  the  sign  of  multiplication  (x). 

7.  Find  answers: 

a  486  is  what  per  cent  of  3888? 

b  What  per  cent  of  284  is  710? 

c  $7.77  is  what  per  cent  of  $129.50? 

d  What  per  cent  of  384  A.  is  320  A.? 

e   \Z%  is  what  per  cent  of  37^? 

/  What  per  cent  of  12^  is  83%? 

g  $137.70  is  what  per  cent  of  $17,000? 

8.  What  per  cent  of  hits  is  made  by  a  ball  player 
who  makes    (a)    134  hits  out  of    443  attempts?     (b) 
146  hits  out  of  487  attempts? 


METHOD 
.3024 

.2998 

(a)     443)134.0              (6) 
1100 
214 
30.2%  Ans. 

487)146.0 
4860 
4770 
30.0%  Ans. 

Carry  out  the  division  to  the  fourth  decimal  place. 
Drop  the  latter  if  less  than  5;  increase  the  third  place 
by  1  if  the  fourth  figure  is  5  or  more. 

A  rate  expressed  as  a  mixed  decimal  generally 
indicates  an  approximation.  Thus  30.2%  does  not 
necessarily  mean  exactly  30X%;  30.0%  may  mean 
that  a  more  exact  rate  is  somewhere  between  29.95  % 
and  30.05%. 


68  WALSH'S  BUSINESS  ARITHMETIC 

To  find  the  number  of  hits  represented  by  30.2% 
of  443,  change  133.786,  the  product  of  .302  X  443, 
to  the  nearest  integer,  134.  To  find  the  number 
represented  by  30%  of  487,  change  146.1,  the  product 
of  .3  X  487,  to  the  nearest  integer,  146. 

Rates  given  in  statistical  tables  are  sometimes 
carried  to  the  nearest  hundredth,  one  or  two  decimal 
ciphers  being  annexed,  for  the  sake  of  uniformity, 
even  when  the  rate  is  an  integer. 

Baseball  records  are  generally  printed  as  three-place  decimals;  such  as, 
.380,  .295,  .400,  etc.  These  are  generally  spoken  of  as  380,  295,  400,  etc., 
omitting  the  denomination  "thousandths."  A  thoughtless  person  may  say 
"380  per  cent,"  and  a  careless  newspaper  may  use  the  expression  "Per 
Cents "  at  the  head  of  the  table  of  records,  when  the  latter  contain  the 
prefixed  decimal  point. 

9.  Find  the  records  of  each  of  the  following  players, 
giving  the  rate  as  a  decimal  to  the  nearest  thousandth. 

a  Cobb,  195  hits  out  of  507  times  at  bat 

b  Sisler,  187  hits  out  of  530  times  at  bat 

c  Felsch,  160  hits  out  of  511  times  at  bat 

d  Speaker,  159  hits  out  of  457  times  at  bat 

e  Veach,  149  hits  out  of  491  times  at  bat 

/  Chapman,  149  hits  out  of  488  times  at  bat 

g  Lewis,  143  hits  out  of  466  times  at  bat 

h  Roth,  130  hits  out  of  429  times  at  bat 

i  Whose  is  the  better  record,  Roth's  or  Veach's? 

10.  Find  results  as  per  cents  correct  to  one  decimal 
place: 

In  these  examples  carry  the  division  out  to  only  three  decimal  places. 
Give  each  answer  as  a  per  cent  and  a  tenth.  The  nearest  tenth  is  not 
called  for. 

a  What  per  cent  of  1325  is  476? 

b  $380.50  is  what  per  cent  of  $250.75? 

c  What  per  cent  of  187  A.  is  83  A.? 


BUSINESS  CALCULATIONS  69 

d  692  bu.  is  what  per  cent  of  463  bu.? 
e  What  per  cent  of  $191.75  is  $47.50? 
/  165  Ib.  is  what  per  cent  of  3329  lb.? 
g  What  per  cent  of  365  da.  is  56  da.? 
h  $33.92  is  what  per  cent  of  $283.11? 
i  What  per  cent  of  431  mi.  is  653  mi.? 
j  823  gal.  is  what  per  cent  of  237  gal.? 

FINDING  THE  BASE 
PREPARATORY  EXERCISES 

1.  What  should  be  the  amount  of  a  girl's  sales  to 
entitle  her  to  a  commission  of  $6  when  the  rate  is  5  %? 

2.  How  much  must  a  man  invest  to  obtain  an  annual 
income  of  $1200  when  the  investment  pays  4  %  a  year? 

3.  Give  the  cost  of  an  article  when  $30  is  (a)  %  of 
the  cost;    (b)  %  of  it;    (c)  %  of  it;    (d)  %  of  it;    (e)  % 
of  it;  (/)  %  of  it. 

4.  What  is  the  cost  of  goods  when  profits  of  $120 
are    (a)    25%    of   the    cost?      (6)    33%%?     (c)  20%? 
(d)  16%%?     (e}  12%%?     (/)  6%%? 

SIGHT  EXERCISES 

1.  Give  the  base: 

a  25  is  12%  %  of  what?  b  34  is  20  %  of  what? 

c  32  is  33%  %  of  what?  d  66  is  30  %  of  what? 

e  24  is  37%  %  of  what?  /  72  is  40  %  of  what? 

g  36  is  66%  %  of  what?  h  48  is  60  %  of  what? 

i   30  is  83%  %  of  what?  j  56  is  70  %  of  what? 

2.  Give  answers: 

a  24  is  3  %  of  what?  6  24  is  120  %  of  what? 

c  32  is  4  %  of  what?  d  30  is  125  %  of  what? 

e  30  is  5  %  of  what?  /  50  is  200  %  of  what? 

g  36  is  6  %  of  what?  h  99  is  110  %  of  what? 

i  21  is  7  %  of  what?  j   60  is  300  %  of  what? 


70  WALSH'S  BUSINESS  ARITHMETIC 

3.   Give  answers: 

a  Base,  $300;  rate,  6  %.     Percentage? 
b  Rate,  25%;  percentage,  $30.     Base? 
c  Percentage,  $60;  base,  $120.     Rate? 
d  Base,  $250;  percentage,  $50.     Rate? 
e  Rate,  33%%;  percentage,  $12.     Base? 
/  Percentage,  $24;  rate,  20%.     Base? 

WRITTEN  EXERCISES 

1.   A  dealer's  profit  of  $2480  is  15#%of  his  invest- 
ment.    What  is  his  investment? 


METHOD 

.15%  X  Investment  =  $2480 
Investment  =  $2480  -^  .155 
$16,000  Ans. 

Since  .15%  times  the 
investment  is 
$2480,   the   invest- 
ment  is  found   by 
dividing   $2480  by 
.155. 

/155)$2480/000. 
930 
0 

To  find  the  BASE,  divide  the  PERCENTAGE  by  the  RATE 
expressed  as  a  decimal. 

2.  How   much    insurance    can    a   property    owner 
obtain  for  $37.50  when  the  rate  is  %%? 

.00%  of  ?    =  $37.50         ?  =  $37.50  *  .00% 

3.  How  much  must  be  an  agent's  sales  to  give  him 
a  commission  of  $106.20  when  the  rate  is  %%%  of  the 
sales? 

4.  How  much  must  be  loaned  at  5%%  per  year  to 
realize  $27.50  interest  annually? 


BUSINESS  CALCULATIONS  71 

5.  This  year's  register  is  15  %  greater  than  that  of 
last  year.     What  was  last  year's  register  if  there  is  an 
increase  this  year  of  24  pupils? 

6.  There  were  promoted  at  the  end  of  the  term 
240  pupils,  which  was  96  %  of  the  register.    What  was 
the  register? 

NOTE:  If  the  resulting  per  cent  is  not  an  integer,  express  it  as  a  mixed 
number  when  the  fractional  part  contains  small  numbers;  otherwise,  express 
it  as  a  mixed  decimal  to  nearest  tenths,  even  when  the  latter  is  a  cipher  (0) . 

7.  Find  the  per  cent  of  butter  fat  in  milk  when 
2480  pounds  of  the  latter  yield  136%  pounds  of  butter 
fat. 

8.  A  manufacturer  expended  in  a  year  $43,625  for 
materials,  $46,750   for   labor,  and  $12,375   for   other 
manufacturing  expenses,     (a)  Find  the  total  cost  of 
the  product.     What  per  cent  of  the  total  cost  was 
paid  (b)  for  materials  ?    (c)  For  labor  ?   (d)  For  other 
manufacturing  expenses? 

9.  When  the  dressed  weight  of  a  steer  is  56%  of  its 
live  weight,  what  should  be  the  live  weight  to  give 
the  butcher  868  pounds  of  meat? 

10.  What  per  cent  of  a  long  ton  (2240  pounds)  is 
a  short  ton  (2000  pounds)? 

11.  A   merchant  has   $27,500  with   which   to  pay 
debts  amounting  to  $35,000.     What  per  cent  of  his 
indebtedness  can  he  pay? 

12.  A  school  having  725  pupils  on  register  trans- 
ferred 87  of  them  to  a  neighboring  school.     What  per 
cent  of  the  pupils  were  transferred? 

13.  (a)  Last  year  a  planter  raised  an  average  of  360 
pounds  of  cotton  to  the  acre.     This  year's  yield  is 


72  WALSH'S  BUSINESS  ARITHMETIC 

54  pounds  greater.  What  is  the  rate  of  increase? 
(b)  WThat  is  the  rate  of  decrease  when  a  yield  of  414 
pounds  to  the  acre  is  a  decrease  of  54  pounds? 

14.  WTiat  does  a  merchant  receive  for  a  parlor  set 
bought  for  $184.50  and  sold  (a)  at  an  increase  of  40%? 
(b)  At  a  loss  of  6  %? 


METHOD 

(a)  $184.50  (b)  $184.50 

+  40%  73.800  -6%  11.0700 

Ans.  $268.30  Ans.  $173.43 

(a)  Find  4  tenths  of  $184.50  by  multiplying  the 
latter  by  4,  writing  the  first  figure  of  the  product 
as  thousandths  (3  decimal  places). 

(b)  Find    6    hundredths    by    multiplying    $184.50 
by  6,  writing  the  first  figure  of  the  product  as  ten- 
thousandths  (4  decimal  places). 


15.  Find  the  selling  prices  of  the  following: 

a  Cost,  $47.60;  gain,  30%  of  cost. 

b  "  $23.40;  loss,   15%  "      " 

c  "  $37.50;  gain,  60%  "     " 

d  "  $92.64;  loss,   25%  "     " 

e  "  $83.20;  gain,  30%  " 

/  "  $76.15;  loss,   20%  " 

g  "  $41.50;  gain,  18%  " 

h  "  $56.25;  loss,  12%  " 

i  "  $83.90;  gain,  40%  " 

j  "  $12.50;  loss,  24%  " 

16.  (a)  W^hat  per  cent  of  the  cost  is  gained  by  a 
man  when  he  sells  for  $420  a  horse  that  cost  him  $360? 


M 
M 

M 

7o 

M 
U 


BUSINESS  CALCULATIONS  73 

(6)  What  per  cent  of  the  cost  does  a  man  lose  by  selling 
for  $360  a  horse  that  cost  him  $420? 

17.  What  per  cent  of  the  cost  is  made  on  an  article 
bought  for  $183.75  and  sold  for  $221.75? 

18.  Find  the  per  cent  of  the  cost  that  is  gained  or 
lost  on  each  of  the  following: 

a  Cost,  $356;  selling  price,  $475 

b  Selling  price,  $129.50;   cost,  $87.75 

c  Cost,  36  i;   selling  price,  46  £ 

d  Selling  price,  $123;   cost,  $150 

e  Cost,  87}^;   selling  price,  83^ 

f  Selling  price,  $250;   cost,  $260 

g  Cost,  $25.60;   selling  price,  $30 

h  Selling  price,  $84;  cost,  $75 

i  Cost,  $1.50;   selling  price,  $1.63 

j  Selling  price,  33}^;   cost, 


19.  What  per  cent  of  the  cost  is  made  on  goods 
sold  for  $260,  in  which  (a)  the  gain  was  $40?    (6)  The 
loss  was  $30? 

First  find  the  cost,  which  is  in  (a)  $40  less  than  the  selling  price,  in 
(6)  $30  more  than  the  selling  price. 

20.  What  does  a  merchant  lose  on  an  article  sold 
for  $118.90,  which  was  18%  less  than  cost? 

$118.90    .  $118.90  x  .18 

Cost  =  —  ^—  ;  loss  =  18%  of  cost  =  -        ^ 

Do  not  find  the  cost.     After  writing  it  as  shown  above,  write  .18  after 
it  as  a  multiplier. 

21.  Find  the  selling  price  of  goods  costing  $125  and 
sold  at  an  advance  of  36  %. 

22.  What  per  cent  above  the  cost  was  made  on  sales 
amounting  to  $896.10,  on  which  the  profit  was  $26.10? 


74  WALSH'S  BUSINESS  ARITHMETIC 

23.  How  much  was  lost  on  sales  of  $142.80  when 
goods  were  sold  15%  below  cost? 

24.  What  per  cent  of  the  cost  was  realized  on  goods 
costing  $245  and  sold  at  $300? 

25.  When  20%  of  the  cost  was  lost  on  goods  sold 
for  $324,  what  was  the  cost? 

RATE  OF  PROFIT 

A  bank  official  who  had  bought  a  house  for  $3600 
and  sold  it  for  $4500  would  possibly  consider  that, 
in  making  $900  by  the  transaction,  he  had  realized 
25%  on  his  investment  of  $3600.  A  merchant,  how- 
ever, would  look  upon  it  as  a  gain  of  20%,  meaning 
that  of  the  $4500  received  20  %  was  profit. 

A  dry  goods  dealer  who  fixes  his  selling  price  of 
silk  at  an  advance  of  25%  above  the  invoice  cost  of 
$1.60  per  yard,  thinks  of  his  profit  as  20  %  of  the  selling 
price  of  $2.  When,  therefore,  he  makes  an  estimate 
of  his  gross  profits  on  sales  of  $4000,  he  takes  20  %  of 
the  latter  as  the  profit,  even  though  he  may  have 
been  taught  in  school  that  he  should  first  find  the 
cost  of  the  goods,  $3200,  by  dividing  $4000  by  1.25, 
and  then  deduct  this  quotient  from  $4000  to  ascertain 

the  profit. 

SIGHT  EXERCISES 

1.  When  Mr.  Jones  sells  for  $27  a  table  that  cost 
him  $18,  what  fraction  (a)  of  the  selling  price  is  the 
cost?  (6)  Of  the  cost  is  the  selling  price?  (c)  Of 
the  cost  is  the  profit?  (d)  Of  the  selling  price  is  the 
profit? 

NOTE:  The  fraction  may  be  an  improper  one. 


BUSINESS  CALCULATIONS  75 

2.  Give  the  fraction  the  selling  price  is  of  the  cost 
in  each  of  the  following: 

Cost       S.P.  Cost      S.P.  Cost          S.P. 

a  $24         $36  b  bit        %%i  c  $1.60         $2.00 

d  $15        $18  e  18£        21  jf  /  $1.60         $1.80 

3.  Give  the  per  cent  the  selling  price  is  of  the  cost 
in  each  of  the  following: 

Cost      S.P.  Cost      S.P.  Cost  S.P. 

a  $32         $48  b  l&£         24ff  c  $2.80          $3.50 

d  $60         $72  e  54^         63^  /  $1.20         $1.35 

4.  For   each   of   the   following   transactions,    state 
what  fraction  the  profit  is  (I)  of  the  cost,  (II)  of  the 
selling  price: 

Cost      S.P.  Cost      S.P.  Cost  S.P. 

a  $50         $75  b  36^         48^  c  $1.20         $1.50 

d  $20         $24  e  60^         70^  /  $2.40  2.70 

5.  For  each  of  the  following,  state  what  per  cent 
the  profit  is  (I)  of  the  cost,  (II)  of  the  selling  price: 

Cost    •  S.  P.  Cost      S.  P.  Cost  S.  P. 

a  $40         $60  b  60^         80^  c  $3.60          $4.50 

d  $30         $36  e  36^         42^  /  $4.20          $4.80 

6.  Give  the  per  cent  of  profit  on  the  selling  price 
that  corresponds  to  each  of  the  following  per  cents  of 
the  cost: 

a  150  %         b  133K  %       c  125  %         d  120  % 

e  116%% 


76  WALSH'S  BUSINESS  ARITHMETIC 

NET  PROFIT 

In  the  foregoing  examples  the  gross  profit  has  been 
considered.  This  is  the  difference  between  the  invoice 
price  of  an  article  and  the  sum  received  for  it.  In 
determining  the  net  profits  of  a  business,  all  expenses 
incurred  in  buying  and  in  selling  must  be  taken  into 
account. 

WRITTEN  EXERCISE 

The  books  of  H.  L.  Mathews  &  Co.  show  the  follow- 
ing receipts  and  expenditures: 

Gross  receipts  from  sales  $159,000 

Expenditures  for  merchandise  $106,000 

Salaries,  commissions,  etc.  31,800 

Rent,  taxes,  etc.  6,360 

Other  expenses  2,120         (a) 

Net  profit  (6) 

Find  (a)  total  expenditures,  and  (6)  the  net  profit. 

(c)  What  per  cent  of  the  total  receipts  is  the  net 
profit?    What  per  cent  of  the  total  receipts  is  expended 

(d)  for  merchandise?    (e)  For  salaries,  commissions,  etc. ? 
(/)  For  rent,  taxes,  etc.?    (g)  For  other  expenses? 


CHAPTER  TWO 


COMMERCIAL    DISCOUNTS 
CASH  DISCOUNT 

The  following  is  an  invoice  for  a  half  chest  of  gun- 
powder tea  and  one  of  imperial  tea.  The  accompany- 
ing marks  designate  the  grade  of  each. 

The  gross  weight  of  each  is  given,  also  the  tare  and 
the  net  weight. 

The  terms  of  the  sale  state  that  payment  is  due  in 
4  months,  and  that  a  discount  of  3%  of  the  face  of 
the  bill  will  be  allowed  if  payment  is  made  in  10  days. 


SAN  FRANCISCO,  CAL.,  January  21,  1920 
Messrs.  John  Ahern  &  Co., 
San  Bernardino,  Cal. 

Bought  of  S.  Collard  &  Co., 

104  Front  St. 
Terms  4  mo.;  cash  10  da.,  less  3% 


1  h/c  Gunp.               \T/ 
93-22-71              X                 .38 
/«6\ 
1  h/c  Imp.                   //^^ 
96-22-74           <^L.W.C^>     .35 

WRITTEN  EXERCISES 

1.  Copy  and  complete  the  foregoing  invoice. 

2.  (a)  How   much  discount  will  be  allowed  if  the 
invoice  is  paid  in  January,  1920?     (6)  What  sum  will 
settle  the  invoice  on  this  date? 

The  terms  are  sometimes  expressed  in  a  shortened  form;  60-2/30, 
meaning  that  a  credit  of  60  days  is  granted,  with  discount  of  2  %  for  pay- 
ment within  30  days.  . 

77 


78  WALSH'S  BUSINESS  ARITHMETIC 

3.  Find  the  sum  that  will  settle  each  of  the  follow- 
ing bills  (invoices)  on  the  date  specified: 

a  Bought  Nov.  16,  1920  b  Bought  Mar.  23,  1921 
2  library  tables  at  $9.65  7  cases  milk  $3.50 

4  parlor  tables  at  $2.50  3      "        "     4.20 

Terms  60-2/30  Terms  30-1^/10 

Paid  Dec.  4,  1920  Paid_Apr.  4,  1921 

The  terms  of  the  following  in  voice,  60  -  2/10  -  1/30 
indicate  a  credit  of  60  days,  a  discount  of  2  %  for  pay- 
ment within  10  da,ys,  or  1  %  for  payment  within  30 
days. 

4.  W.  S.  Goodnough  buys  of  John  Ziegler  &  Co., 
on  January  7,  1920,  1%  doz.  milk  kettles  @  $18  per 
dozen,  and  2%doz.  dippers  @  $2.10  per  dozen.     What 
sum  will  settle  the  bill   (a)   on  February   14,   1920? 
(b)  On  January  12,  1920?     (c)  On  March  12,  1920? 

5.  A  grocer  bought  on  March  1,  1921,  1500  pounds 
of   coffee   at    18.75^   per   pound.     Find    (a)  the   net 
amount  of  the  bill ;  that  is,  the  sum  due  at  the  expi- 
ration of  the  credit  period,    (b)  The  sum  required  to 
pay  the  bill  on  March  10  with  1%  discount,     (c)  The 
sum  payable  on  March  13,  if  the  seller  allows  a  dis- 
count for  48  days  at  the  rate  of  6  %  per  year. 

TRADE  DISCOUNTS 
"List  Prices" 

Many  manufacturers  issue  catalogues  describing 
their  products.  The  prices  given  in  these  catalogues 
(list  prices)  are  much  higher  than  those  actually 
charged  to  dealers,  being  subject  to  a  trade  discount. 


BUSINESS  CALCULATIONS 


79 


which  is  not  specified  in  the  catalogue,  but  is  contained 
in  a  discount  sheet  supplied  only  to  customers.  When 
rates  are  changed,  a  new  discount  sheet  is  sent  out. 

The  following  bill  (invoice)  for  sewer  pipes  provides 
for  specified  trade  discounts.  A  cash  discount  of  2%  of 
the  net  amount  is  offered  for  payment  within  15  days. 

The  net  amount  of  a  bill  is  generally  taken  as  the 
sum  required  to  settle  the  bill  at  the  end  of  the  credit 
period,  viz.,  $188.24  in  the  one  given  below;  that  is, 
the  sum  remaining  after  the  deduction  of  the  trade 
discounts. 

Denver,  Colo.,  April  26,  1920 
Messrs.  Tully  &  Larkin 

Manitou,  Colo.  Order  #53516 

Bought  of 
AMERICAN  SEWER  PIPE  COMPANY 

Terms:  30  da.;  15  da.  less  2% 


Buyer's 
Order 

Pieces 

Size 

Kind 

List 
Price 

Gross 
Amt. 

Net 

Total 

No. 

1149 

400 

6" 

Pipe  #2 

80 

320 

_ 

15 

15" 

"      " 

2 

70 

(a) 

15 

24* 

«      « 

6 

50 

(b) 

458 



Dis 

ct.  72% 

(£) 

128 

24 

250 

8" 

Pipe  #3 

80 

(d) 

Dis 

ct.  70  % 

140 

— 

60 

— 

188 

24 

WRITTEN  EXERCISES 

1.  Copy  the  foregoing  bill,  filling  out  the  missing 
extensions;   (a),  (6)  and  (d),  also  (c)  the  missing  dis- 
count. 

2.  What  sum  will  pay  this  bill  on  May  25? 


80  WALSH'S  BUSINESS  ARITHMETIC 

3.  Find  the  net  amount  of  a  bill  for  300  pieces  of 
8"  pipe  at  $1.10,  and  50  pieces  of  12"  pipe  at  $2,  less 

74%. 

SIGHT  EXERCISES 

1.  What  is  (a)  the  discount  on  a  purchase  of  pipe 
listed  at  $250  when  the  rate  is  72  %?     (6)  The  net  price? 
(c)  What  per  cent  of  the  list  price  is  the  net  price? 

2.  When  the  discount  is  70%  (a)  what  per  cent  of 
the  list  price  is  the  net  price?     (6)  What  is  the  net 
price  of  an  article  listed  at  $333? 

3.  When  the  discount  is  90  %,  what  is  the  net  price 
of  an  article  listed  at  $475? 

4.  Give  answers : 

a  List  price,  $150;  discount  rate,  15  %  Discount? 

b  "  "  203;  "  30%  Net  price? 

c  "  "  320;  "  20%  Discount? 

d  "  "  110;  "  40%  Net  price? 

e  "  "  284;  "  50%  Discount? 

/  "  "  560;  "  25%  Net  price? 

g  "  "  675;  "  10%  Discount? 

h  "  "  222;  "  60%  Net  price? 

i  "  "  102;  "  18%  Discount? 

j  313;  90%  Net  price? 

COMPOUND   DISCOUNTS 

Some  discount  sheets  offer  two,  three,  or  more, 
successive  discounts  on  a  given  article:  25  and  5%, 
for  example;  SS£  15,  and  10%;  35, 10, 5,  and 2^%;  etc. 

In  expressing  these,  the  per  cent  sign  (%)  is  written  only  after  the  last 
rate  of  a  series.  On  bills,  these  compound  discounts  are  frequently  written 
thus:  25/5,  331/15/10,  35/10/5/2,  without  the  per  cent  sign. 

The  general  method  of  determining  the  net  price 
of  an  article  subject  to  a  compound  discount  is  shown 
in  the  following  example.  The  first  discount  is  taken 


BUSINESS  CALCULATIONS  81 

on  the  list  price,  the  next  is  taken  on  the  remainder 
left  after  the  deduction  of  the  first  discount,  the 
next  is  taken  on  the  remainder  left  after  the  deduction 
of  the  second  discount,  etc. 

WRITTEN  EXERCISES 

1.  Find  the  net  price  of  an  article  "listed"  at  $102, 
and  subject  to  discounts  (a)  of  25  and  5%;  (6)  of  33%, 
15,  and  10%;  (c)  of  35,  10,  5,  and  2%%. 


METHOD 

(a)  List  price  $102.        (b)  List  price 

Less  25%      25.50         Less  33%%  34. 


Remainder  $76.50          1st  Remainder    $68.00 
Less  5%          3.825       Less  15  %  10.20 

Net  price    $72.68         2d  Remainder     $57.80 

Less  5%  2.89 

Net  price  $54.91 

(c)  List  price  $102. 

Less  35  %  35.70 

1st  Remainder    $66.30 
Less  10%  6.63 

2d  Remainder     $59.67 
Less  5  %  2.983 

3d  Remainder     $56.687 
Less  2%%  1.417 

Net  price  $55.27 

Test  each  result  by  taking  the  separate  discounts 
in  a  different  order;  in  (a)  5  and  25%;  in  (b)  5, 
15,  and  33%%;  and  in  (c)  2%,  5,  10,  and  35%. 


82  WALSH'S  BUSINESS  ARITHMETIC 

2.  Find  the  net  price  of  each: 

List  price  Discount  Rate  List  price          Discount  rate 

a  $104  33%  and  15  %  b  $200  35,  10,  and  5  % 

c     220  25  and  10  %  d    300  33%,  15,  and  10  % 

e     310  45  and  5  %  /     100  45,  10,  and  2%% 

g     201  15  and  10  %  /i     150  15,  5,  and  3  % 

i     142  35  and  5  %  j     400  25,  10,  and  10  % 

3.  What  is  the  net  price  of  an  article  listed  at  $275 
and  subject  to  a  discount  of  60  and  20  %? 


METHOD 

r\nr*f>,      <fe<?7^        (n"\  Use  as  successive  multipliers  the 

price        >Z15.  complements  of  the  per  cents  con- 

40%  of  (a)      110.       (b)  stituting  the  discount  rate 

80%  of  (6)  $  88.  Net  price 


To  obtain  the  complement  of  a  per  cent,  deduct  it  from  100%.    Thus: 
25  %  is  the  complement  of  75  %,  95  %  is  the  complement  of  5  %,  etc. 

4.  Write  from  the  book  the  net  price  of  each  of  the 
following: 

List  price  Discount  List  price  Discount  List  price  Discount 

a  $123.40     20%          b  $312.20     40%  c  $369.36     66%% 

d    211.15     30%  e    156.84     50%  /    248.24     87%% 

g    486.40     75%  h    215.25     60%  i    486.12     83%% 

5.  Using  the  complements  of  the  given  rates,  find 
the  net  price  of  each  of  the  following: 

a  $420;  60  and  20  %  6  $465;  50  and  30  %  c  $450;  66%  and  20  % 
d  352 ;  50  and  30  %  e  352;  75  and  30%  /  864;  87%  and  30% 
g  275;  40  and  40  %  h  576;  60  and  30%  i  648;  83% and  20% 


BUSINESS  CALCULATIONS 


83 


6.  Copy  and  complete  the  following  bill  for  iron 
pipes.  Take  the  quantity  given  in  feet  and  inches  at 
the  list  price  per  foot. 

Use  the  "gross"  column  only  when  more  than  one 
item  is  subject  to  the  same  discount. 


INTERNATIONAL   TUBE  COMPANY 


Birmingham,  Ala. 
SOLD  TO  Thomas  N.  DeLaney, 

Wilmington,  N.  C. 
Terms  60-2/10.    Route  S.  A.  L. 


March  29,  1921 
Agency  Order  5188 
Customer's  Order  3716 
Car  S.  A.  L.  75190 
F.o.b.  Wilmington 


Bdls. 

Size 

Description 

Feet 

In. 

List 
Price 

Gross 

Total 

Dis. 

Net 

15 

3  '/ 

Wro't  Pipe 

5322 

6 

.10 

532 

25 

60-20 

to 

15 

3  " 

(C 

2093 

3 

.20 

418 

65 

25 

r 

( 

2  82 

4 

.30 

804 

70 

1223 

35 

70-20 

(/) 

15 

¥ 

« 

3652 

9 

.16 

(a) 

75-20 

(9) 

25 

if 

" 

1562 

— 

.40 

(&) 

25 

ir 

1534 

8 

.50 

J«L 

— 

(d) 

70-30 

(h) 

— 

K4 

NOTE:  F.  o.  b.  Wilmington  means  that  the  goods  are  delivered  at  the 
R.  R.  station  at  Wilmington  without  charge  for  cartage  at  Birmingham 
or  freight  charges  to  Wilmington.  The  buyer  is  expected  to  remove  them 
promptly  from  the  freight  car  upon  notification  of  the  arrival  of  the  latter. 
The  invoice  gives  the  designation  of  the  car  S.  A.  L.  (Seaboard  Air  Line) 
and  its  number. 

SIGHT  EXERCISES 
1.   Give  the  per  cent  of  the  list  price  equal  to: 


a  40  %  of  80  %  of  it. 
c  50  %  of  70  %  of  it. 
e  25  %  of  70  %  of  it. 


6  33%%  of  80%  of  it. 
d  12K%of  70%  of  it. 
/  16%%  of  80%  of  it. 


84  WALSH'S  BUSINESS  ARITHMETIC 

2.  What  per  cent  of  the  list  price  is  the  net  price 
when  the  discount  rate  is: 

a  20  and  10  %?  b  30  and  20  %?  c  75  and  20  %? 

d  40  and  20  %?  e  50  and  10  %?  /  66%  and  10  %? 

0  30  and  10  %?  A  40  and  30  %?  i  87^  and  20  %? 
j   60  and  20  %?  fc  70  and  10  %?  /  83#  and  40  %? 

3.  Give  the  net  price  of  each  of  the  following: 

List  price          Discount  List  price  Discount 

a  $444  75  and  20  %  b  $312  66%  and  10  % 

c  $695          87/2  and  20  %  d  $547          83%  and  40  % 

4.  What  single  discount  equals  a  double  discount  of 
40  and  20%? 

When  the  discount  is  40  and  20%,  the  net  price  is  60%  of  80%  of  the 
list  price;  that  is,  it  is  48%  of  the  list  price.  The  discount  is,  therefore, 
52%  of  the  list  price  (100%T48%). 

A  shorter  method  to  obtain  the  latter  is  to  deduct  from  the  sum  of  the 
successive  discounts  their  product. 

(40%  +  20%)  -  (40%  of  20%)  =  60%  -  8%  =  52% 

6.  Give  the  single  discount  equal  to  each  of  the 
following : 

a  60  and  10%  b  50  and  40%  c  90  and  10%  d  33%  and  10% 
e  80  and  20  %  /  60  and  30  %  g  70  and  20  %  h  66%  and  10  % 

1  70  and  10  %    j  80  and  10  %     k  60  and  40  %    I  83%  and  10  % 

6.   Which  is  the  better  discount  for  the  buyer? 

a  60  and  10  %  or  50  and  20  %  b  40  and  20  %  or  30  and  30  % 
c  80  and  20  %  or  70  and  30  %  d  50  and  40  %  or  60  and  30  % 
e  50  and  30  %  or  40  and  40  %  /  30  and  20  %  or  40  and  10  % 

WRITTEN  EXERCISES 

1.  Two  manufacturers  list  a  certain  grade  of  piano 
at  $975.  One  offers  a  discount  of  60  and  20%;  the 
other  offers  50  and  30%.  (a)  What  per  cent  of  the 
list  price  does  the  purchaser  save  by  taking  the  better 


BUSINESS  CALCULATIONS  85 

offer?     (6)  How  much  money  does  he  save  on  each 
piano  purchased  at  the  lower  rate? 

2.   What  single  discount  is  equal  to  a  discount  of 
45,  10,  and  5  %? 


METHOD 

A  discount  of  45  and  10%  =  45%  +  10%  -  (10% 
of  45%)  =  55%  -  4.5%  =  50.5%;  a  discount 
of  50.5  and  5  %  =  (50.5  %  +  5  %)  --  (5%  of 
50.5%)  =  ? 


First  combine  two  of  the  successive  discounts  into  an  equivalent  single 
discount;  then  combine  the  latter  and  the  third  successive  discount  into  an 
equivalent  single  discount. 

3.  Find  the  single  discount  equivalent  to  each  of 
the  following: 

a  40,  10,  and  10%  6  50,  20,  10,  and  5% 

c  30,  20,  and  10%  d  60,  30,  10,  and  5% 

4.  What  per  cent  of  the  list  price  is  the  net  price 
when  the  discount  rate  is  50,  30,  and  20%? 


METHOD 


Using  the  complements,  take  50  %  of  70  %  of  80  %, 
which  can  be  simplified  by  taking  50%  of  80% 
of  70%. 


5.   What  per  cent  of  the  list  price  is  the  net  price 
when  the  discount  rates  are,  respectively? 

a  75,  20,  and  10  %  6  87&  20,  and  10  % 

c  66%,  10,  and  5  %  d  8S&  40,  and  5  % 

e  45,  10,  and  5  %  /  60,  30,  and  10 


86 


WALSH'S  BUSINESS  ARITHMETIC 


0 

55% 

lessKo    5.5 

49.5  % 

less  Ko    2.475 

47.025  % 


METHOD 

Many  accountants  prefer  the  de- 
duction of  Xo  to  the  multiplication, 
by  90%.  All  prefer  the  deduc- 
tion of  Ko  to  the  multiplication  by 
95%. 

Begin  with  55  %,  the  complement 
of  45%. 


6.  What  per  cent  of  the  list  price  is  the  net  price 
when  the  discount  rates  are,  respectively? 

a  55,  15,  and  5%  b  45,  15,  10,  and  5% 

To  be  enabled  to  make  calculations  more  rapidly,  bill  clerks  use  tables 
showing  the  per  cent  of  the  list  price  to  be  taken  in  determining  the  net 
price  of  articles  subject  to  a  compound  discount.  The  table  also  gives 
the  equivalent  single  discount. 

The  following  shows  a  portion  of  one  of  the  pages: 

COMPOUND   DISCOUNT  TABLE 


30 

40 

50 

60 

Supplementary 

Discounts 

Dis. 

Net 

Dis. 

Net 

Dis. 

Net 

Dis. 

Net 

.30 

.70 

.40 

.60 

.50 

.50 

.60 

.40 

5 

.335 

.665 

.43 

.57 

.525 

.475 

.at 

.38 

10 

.37 

.63 

.46 

.54 

.55 

.45 

.64 

.36 

10 

5 

.4015 

.5985 

.487 

.513 

.5725 

.4275 

.658 

.342 

15 

.405 

.595 

.49 

.51 

.575 

.425 

15 

5 

.43475 

.  -5i;.>*5 

.5155 

.4845 

.59625 

.  40375 

15 

10 

.4645 

.535 

.541 

.459 

.6175 

.3825 

15 

10 

5 

.491275 

.508725 

.56395 

.43605 

.636625 

.363375 

20 

.44 

.56 

.52 

.48 

20 

5 

.468 

,m 

.544 

.456 

20 

10 

,4M 

.504 

.568 

.432 

20 

10 

.5212 

.4788 

.5896 

.4104 

BUSINESS  CALCULATIONS  87 

7.  Calculate    (a)    the    missing    net    rates;    (b)    the 
missing  equivalent  single  discounts. 

Check  results  by  finding  the  total  of  (a)  and  (6)  in 
each  case. 

8.  Find 'the  net  price  of  goods  subject  to  a  discount 
of  30,  15,  10,  and  5%  and  listed  (a)  at  $4812;   (6)  at 
$481.20. 

9.  Find  the  net  price  of  each  of  the  following: 

List  price        Discount  List  price  Discount 

a  $568        30,  15,  10,  and  5  %          b  $4812        40,  15,  and  5  % 
c  $328       50,  15,  10,  and  5  %          d  $6408        50,  15,  and  5  % 

10.  Find  the  net  price  of  goods  subject  to  a  discount  of 
30, 15, 10,  and  5  %  and  listed  (a)  at  $3876;  (b)  at  $387.60. 

11.  Find  the  net  price  of  each  of  the  following: 

List  price        Discount  List  price  Discount 

a  $678       30,  15,  10,  and  5  %  b  $4929        40,  15,  and  5  % 

c  $547       50,  15,  10,  and  5  %          d  $6457       50,  15,  and  5  % 


QUANTITY  DISCOUNTS 

Manufacturers  of  certain  staples  frequently  offer 
discounts  dependent  upon  the  quantity  purchased. 

The  following  bill  shows  a  deduction  of  20  cents 
per  100  pounds  from  the  rate  charged  to  smaller  buyers. 

To  withhold  from  other  customers  information  as 
to  the  jobber's  discount,  it  is  inserted  by  means  of  a 
rubber  stamp  only  upon  the  bills  of  such  purchasers 
as  are  entitled  to  receive  it. 


88 


WALSH'S  BUSINESS  ARITHMETIC 


SAN  FRANCISCO,  CAL.,  Jan.  8,  1921 
Messrs.  Jno.  Ziegler  &  Co. 

Bought  of 

THE  PACIFIC  SUGAR  REFINING  COMPANY 
Terms  10  days;  cash  less  1  %  7  days 


Bbl. 


Cases 


Bags 


Fine  #5 

#2 

Less  5i  and  10^  per  100  Ib. 
special  5£    "        " 


Net 


12790 
3200 


(d) 


Price 


7.34 
7.44 


(b) 


(3} 


WRITTEN  EXERCISES 

1.  Copy  the  foregoing  bill,  filling  in  the  omitted 
items. 

2.  Give  the  sum  that  will  settle  it  if  payment  is 
made  on  Jan.  12. 

Sometimes  the  discount  is  conditioned  upon  payment 
within  a  specified  time. 

INDIAN  ROCK,  VA..  Aug.  2,  1919 
Messrs.  Popkins  &  Appich 
Meadow  Springs,  Ohio 

Bought  of  SWIFT  &  STEVENSON 

Manufacturers  of  Building  and  Agricultural  Lime 

130  bbl.  Lime  1.35         $ 
Terms: 

5t  per  bbl.  discount  if  paid  in  10  days  from  date  of  bill, 
60  days  net. 

When  the  allowance  of  a  discount,  or  its  amount,  depends 
upon  the  time  of  payment,  the  seller  does  not  enter  the  dis- 
count upon  the  bill.  The  buyer  makes  the  proper  deduc- 
tion, if  any,  and  sends  his  check  for  the  remainder. 


CHAPTER  THREE 

SIMPLE    INTEREST 

LENDING  MONEY 

Banks,  life  insurance  companies,  individuals,  etc.,, 
are  always  ready  to  loan  their  spare  funds  to  reputable 
borrowers  that  furnish  satisfactory  security  to  pay  a 
fair  rate  for  the  use  of  the  money  and  to  return  the 
latter  at  a  specified  time. 

The  sum  loaned  is  called  the  PRINCIPAL. 

The  sum  paid  for  the  use  of  the  principal,  is  called  the 
INTEREST. 

The  per  cent  of  the  principal  to  be  paid  for  its  use  for  a 
year,  is  called  the  RATE. 

BONDS 

Among  the  borrowers  are  the  United  States,  in- 
dividual states,  counties,  cities,  railroads,  etc.  As 
evidence  of  the  loan  the  lenders  receive  bonds.  These 
documents  specify  the  sum  loaned,  the  rate  of  interest, 
the  time  of  successive  interest  payments  (which  are 
generally  made  half  yearly  or  quarterly),  and  the 
date  for  the  repayment  of  the  principal. 

MORTGAGES,  DEEDS   OF  TRUST 

The  owner  of  a  house  or  a  farm  can  borrow  money 
by  giving,  as  security,  a  mortgage  or  a  deed  of  trust. 

89 


90  WALSH'S  BUSINESS  ARITHMETIC 

Either  document  provides  that  if  the  borrower  defaults 
in  making  payments  of  interest  or  principal,  the 
lender  may  cause  the  property  to  be  sold,  and  the 
amount  due  to  be  paid  him  from  the  proceeds. 

BANK  BOOK 

The  evidence  of  the  loan  to  a  savings  bank  by  a 
depositor  is  given  by  the  entry  made  in  the  latter 's 

pass  book. 

PROMISSORY  NOTES 

A  common  evidence  of  indebtedness  is  a  promissory 
note,  which  every  lender  should  require  in  the  absence 
of  other  security.  This  should  show  the  sum  loaned, 
the  date  of  the  loan,  the  time  for  its  repayment,  the 
rate  of  interest,  etc. 

PREPARATORY  EXERCISES 

1.  A  man  borrows  $1000  on  a  mortgage,  agreeing 
to  pay  annually  for  the  use  of  the  money  6%  of  the 
sum  borrowed,     (a)  How  much  does  he  pay  each  year? 
(b)  If  he  makes  these  payments  every  six  months,  how 
much  is  each  semi-annual  payment? 

2.  At  6  %  per  year,  how  much  should  a  person  pay 
(a)  for  1  month's  use  of  $1000?     (b)  For  2  months' 
use?     (c)  For  5  months'  use? 

3.  A  woman  has  $400  on  deposit  in  a  savings  bank. 
If  the  bank  allows  her  4%  per  year,  how  much  will 
her  money  earn  in  6  months? 

4.  How   much   interest  does   a   girl   receive   every 
3  months  on  a  $50  Liberty  Bond  that  pays  4  per 
cent  interest  each  year? 


BUSINESS  CALCULATIONS  91 

SIGHT  EXERCISES 
1.   Give  the  interest  on  $1200  for  1  year  at: 

a  6%        b  5%        c  7%        d  4^%        e  5%%        f 


g  8%        h  4%        i  3%        j  6^%        k  3%%        I 

2.  Give  the  interest  at  6%  for  1  year  on: 

a  $100       6  $150       c  $200       d  $250       e  $1200      /  $1250 
g  $125       h  $225       i  $325      j   $425       &  $1500       /  $2100 

3.  Give  the  interest  for  1  year  on: 

a  $150  at  5  %  b  $225  at  4  %  c  $1230  at  3  % 

d  $310  at  6  %  e  $510  at  8  %  /  $2010  at  7  % 

4.  Give  the  interest  at  6%  on: 

a  $150  for  2  yr.  6  $300  for  %  yr.  c  $400  for  6  mo. 

for  3  yr.  e  $400  for  %  yr.          /  $600  for  4  mo. 


5.  Give  the  interest  on: 

a  $200  at  &%  %  for  3  yr.  b  $300  at  5  %  for  6  mo. 

c  $120  at  4^  %  for  2  yr.  d  $500  at  4  %  for  3  mo. 

e  $400  at  3%%  for  4  yr.  /  $100  at  6  %  for  8  mo. 

6.  Assuming  the  year  to  consist  of  360  days,  give 
the  interest  at  6%  on  $300  for: 

a  120  da.     6  180  da.     c  90  da.     d  60  da.     e  40  da.    /  20  da. 

WRITTEN  EXERCISES 

1.  (a)  In  3  years  at  5%%,  how  much  interest  does 
a  man  pay  on  a  mortgage  of  $1580?  (5)  How  much 
interest  is  paid  on  a  loan  of  $875  in  4K  years  at  6%? 


92  WALSH'S  BUSINESS  ARITHMETIC 


METHOD 

(a)        Principal    $1580  (6)        Principal  875 

Rate            X  .05#                Rate  X  .06 

790  Interest  for  1  yr.  $52.50 

7900  Time  in  years  X  4^ 

Interest  for  1  yr.  $86.90  2625 

Time  in  years            X  3  21000 

Int.  for  3  yr.        $260.70  Int.  for  4^  yr.      $236.25 

Reverse  the  order  of  the  factors,  in  (a)  multiplying 
$1580  by  3  and  this  product  by  5%;  or,  combine  the 
factors  into  a  single  one,  multiplying  $1580  by 
16&  In  (6)  multiply  $875  by  27. 


To  find  the  interest  multiply  the  PRINCIPAL  by  the 
RATE  (expressed  as  hundredths)  by  the  TIME  (in 
years) . 


2.  Find  the  interest  on: 

a  $756  at  6  %  for  4  yr.  6  $968  at  5  %  for  1%  yr. 

c    359  at  4  %  for  1  yr.  6  mo.  d    642  at  5  %  for  3  yr. 

e    495  at  7  %  for  2M  yr.  /    825  at  6  %  for  2  yr.  3  mo, 

g    508  at  7  %  for  2  yr.  h    287  at  6  %  for  3^  yr. 

i     163  at  9  %  for  3  yr.  4  mo.  j    753  at  4  %  for  1  yr.  4  mo. 

3.  Find  the  interest  at  6%  on: 

a  $120  for  5  mo,  6  $480  for  12  da.  c  $840  for  5  mo.  12  da. 
d  240  for  7  mo.  e  600  for  18  da.  /  960  for  7  mo.  18  da. 
g  360  for  9  mo.  h  720  for  24  da.  i  180  for  9  mo.  24  da. 


BUSINESS  CALCULATIONS  93 

4.   Find  the  interest  on  $180  at  6%  for  (a)  24  da. 
(b)  8  mo.  24  da. 


a 


METHOD 

.03      12  .03 

X  .00  X  ft*  ,   $WP  X  .00  X  264 


Indicate  the  time  in  years  by  writing  it  in  (a)  as 
%o,  and  in  (6)  as  2%0,  changing  8  mo.  24  da.  to 
264  da. 


5.  Find  the  interest  on  $720  at  6  %  for  (a)  25  da. 
(6)  68  da.  (c)  2  mo.  8  da.  (d)  6  mo.  26  da. 

6.  On   March    1,    1917,    Charles   Wilcox   borrowed 
$475  of  Arthur  Washburn,  which  he  agreed  to  repay 
on  demand  with  interest  at  6%.     As  evidence  of  the 
indebtedness  he  gave  Mr.   Washburn   the   following 
note: 


Harvey,  Neb.,  March  1,  1917 
On  demand  after  date,  I  promise  to  pay  to  the  order  of 


Four  Hundred  Seventy-five  %o  .....................  Dollars 

Value  received,  with  interest  at  6%. 


94  WALSH'S  BUSINESS  ARITHMETIC 

Every  six  months  Mr.  Wilcox  paid  %  year's  interest. 

(a)  How  much  was  each  payment?  (6)  How  much 
had  he  paid  in  interest  up  to  and  including  the  pay- 
ment on  March  1,  1920? 

(c)  If  he  settled  the  indebtedness  on  Aug.  18,  1920, 
how  much  would  be  the  sum  of  his  interest  payments? 
(d)  Find  the  interest  on  $475  at  6  %  for  5  mo.  17  da. 


CANCELLATION   METHOD 

(c)  Find  by  compound  subtraction  the  time  1920-vin-18 

for  which  interest  is  paid.  1917-  in-  1 

3-      v-17 
Syr.    =  1080  da 


5  mo.  =    150  " 
17  da.    =      17 
1247 
360 


Change  the  compound  number  3  yr.  5  mo. 
17  da.  to  days  (1247).  Write  360  as  a 
denominator,  thus  expressing  it  in  years 
(in  the  form  of  an  improper  fraction.) 


Indicate  the  product  of  the  principal,  by  the  rate  (in  hundredths), 
by  the  time  in  years;  cancel. 


95      .01 


12 

(d)  The  interest  for  167  days  is  indicated  thus  $475  X  .  06  x  167 

360 

Test 

Test  both  results  by  deducting  (d)  from  (c).    The  difference  should  be 
the  interest  for  3  years. 


When  the  time  is  given  in  years,  months,  and  days, 
take  each  year  as  360  days  and  each  month  as  30  days. 


BUSINESS  CALCULATIONS  95 

7.   Find  the  interest  at  6%: 


a 

$378 

for  3 

mo.  18 

da. 

b 

$840  for 

2  mo 

.9  da. 

c 

156 

"    4 

" 

20 

tt 

d 

252    " 

6 

n 

8  " 

e 

618 

"    8 

" 

17 

n 

f 

507    " 

5 

a 

3   " 

9 

405 

"    9 

" 

28 

ft 

h 

936    " 

7 

a 

6   " 

i 

864 

"    1 

tt 

25 

tt 

3 

738    " 

2 

tt 

5   " 

k 

534 

"    2 

20 

I 

351    " 

1 

tt 

7  " 

8. 

Find  the 

interest  on: 

a 

$426, 

,60 

for 

i  yr. 

3 

mo. 

18  da. 

at 

4% 

b 

318.75 

tt 

2     " 

7 

tt 

15    " 

a 

6% 

c 

563, 

,10 

" 

3     " 

4 

n 

24    " 

" 

5' 

% 

d 

911 

25 

« 

2     " 

8 

tt 

13    " 

a 

3% 

e 

123, 

45 

tt 

1     " 

5 

n 

16    " 

" 

8' 

f 

708, 

,36 

tt 

2     " 

9 

a 

17    " 

a 

7% 

9 

245 

.70 

a 

3     " 

6 

tt 

11    " 

st 

9' 

h 

636 

,30 

a 

2     " 

2 

if 

23    " 

** 

8.' 

% 

i 

824, 

,40 

" 

1     " 

7 

it 

14    " 

'« 

5' 

% 

j 

135.66 

tt 

2     " 

1 

tt 

12    " 

tt 

6% 

9. 

Find  the 

interest  on  : 

a  * 

£378  at  6  % 

for 

140 

da. 

b 

$156  at 

3  %  for  57  da. 

c 

405 

"5% 

tt 

105 

" 

d 

804  " 

6% 

"  69 

e 

980 

"6% 

« 

126 

tt 

f 

252  " 

5% 

"  87     " 

g 

536 

"4% 

tt 

144 

a 

h 

438  <c 

4% 

"  36     " 

i 

618 

"6% 

" 

210 

a 

i 

597  " 

8% 

"  75     " 

k 

734 

"7% 

« 

168 

" 

i 

351  " 

7% 

"  96     " 

10.  Find  (a)  the  interest  on  $386.50  for  3  yr.  7  mo. 
18  da.  at  4K%;  (6)  The  amount  of  $485.60  at  5%  for 
2  yr.  9  mo.  25  da. 


WALSH'S  BUSINESS  ARITHMETIC 


(a)    Principal 
Int.  for  2  yr 
"      "     1   " 
"      "    6  mo. 
"      "     1    " 
"      "  18  da. 


METHOD   BY   ALIQUOT   PARTS 
$386.50 


34.7850 

17.3925 

8.6962 

1.4494 

.8696 


Find  the  interest  for  2  yr.  by  mul- 
tiplying the  principal  by  .09.  Take 
1/2  of  this  as  the  interest  for  1  yr. 
etc.  Note  that  the  interest  for 
18  da.  is  1/10  of  that  for  6  mo. 


3 yr. 7 mo.  18 da.    $63.19    Ans. 


(6)    Principal 
Int.  for  2  yr. 
6  mo. 
3    " 
20  da. 
5    " 


$485.60 
48.56 
12.14 
6.07 
1.3489 
.3372 


For  6  mo.  take  1/4  of  2  yr.  For 
20  da.  take  1/9  of  6  mo.  Since 
the  amount  is  required,  do  not 
draw  a  line  under  the  principal. 


Amt.  2  yr.  9  mo. .  $554 . 06     Ans. 
25  da. 

TEST 
Find  the  interest  by  the  cancellation  method. 

a  $386.50  X  .045  X  1308  b  $485.60  X  .05  X  1015 


To  the  interest  found  in  (6)  by  the  cancellation  method,  add  the  principal. 
This  should  give  the  amount  as  obtained  by  the  aliquot  parts  method. 


Amount  =  Principal  +  Interest 


11.   Find  the  amount  of: 

a  $713.39  at  6%  for  1  yr.  2  mo.  12  da. 
b     246.77    "  5^%  "    3     "3     "     17    " 


c 

525 

.40 

« 

8% 

« 

2 

« 

8 

« 

15 

« 

d 

536 

.81 

« 

9% 

« 

3 

«« 

3 

«< 

24 

« 

e 

809 

.47 

« 

7% 

« 

4 

** 

7 

M 

13 

«« 

f 

234 

.56 

i< 

3^% 

«« 

3 

<i 

9 

« 

18 

« 

g 

923 

.75 

« 

3% 

« 

2 

« 

6 

M 

17 

« 

h 

452 

.09 

« 

5% 

i< 

3 

<« 

9 

t< 

14 

« 

i 

227 

.80 

« 

6% 

«< 

1 

t< 

3 

«( 

23 

«< 

j 

315.50 

« 

4K% 

«< 

i 

2 

« 

4 

{< 

19 

ii 

BUSINESS  CALCULATIONS  97 

k  146.56  at  5  %  for  2  yr.  10  mo.  18  da. 

/  245.70    "  3%     "    3     "  11    "      9  " 

m  318.75    "  3%%  "I      "6    "    25  " 

n  426.60    "  7%     "    2     "     8    "      8  " 

o  563.10    "  9%     "    3      "3    "    20  " 

p  636.30    "  8%     "    2     "     7    "      6  " 

g  708.36    "  5%  %  "1      "5    "    24  " 

r  824.40    "  6%     "    2     "     4    "      7  " 

s  911.25    "  4^%  "3     "9    "    21  " 


12.  A   loan    for    $2500    was    made   July  13,  1916. 
Find  the  amount  that  will  pay  it  on  May  6,  1920, 
including  interest  at  6  %. 

Time  between  Dates 

1920     V       6      When  dates  are  more  than  a  year  apart,  the 
-1916  VII  13      time  is  expressed  in  years,  months,  and  days. 

In  the  following  examples  find  the  time  by  compound 
subtraction. 

13.  Find  the  interest  on: 

a  $930.75  at  6%     from  Dec.   20,  1915  to  Jan.    10,  1919 

b     815.62    "  5^%      "     Mar.  15,  1916    "  Feb.    29,  1920 

c     732.98    "  4  %         "     Jan.    24,  1917    "  May   15,  1918 

d    641.07    "  7%%      "     Aug.   18,  1916    "  Jun.    14,  1919 

e     552.96    "  8  %         "     Jan.    22,  1915     "  Aug.   20,  1918 

/     463.85    "  3%%      "     May  20,  1916    "  Mar.  25,  1920 

g     374.74    "  9  %         "     Feb.   21,  1917    "  Jun.    18,  1921 

h     285.63    "  8^%      "     Jul.     18,  1918    "  Apr.    22,  1922 

i     196.52    "  4  %         "     Sep.    16,  1917    4<  Jul.     30,  1920 

j     207.41    "  6^%      "     Apr.    25,  1916    "  Sep.    24,  1918 

k     398.32    "  6  %         "     Dec.   20,  1915    "  Mar.  16,  1917 

I     489.23    "  3%%      "     Mar.  19,  1914    "  Jan.    18,  1918 


98  WALSH'S  BUSINESS  ARITHMETIC 

14.  (a)  How  many  months  and  days  are  there  from 
July  25,  1919  to  March  16,  1920?  (6)  How  many 
days? 


METHOD 

(6)  6  +  31  +  30  +  31  +  30  +  31  +  31  +  29  +  16  =  ? 

To  the  6  (31-25)  remaining  days  in  July,  add  the 
number  of  days  in  the  other  months  to  February, 
inclusive,  and  the  number  of  days  (16)  expressed 
by  the  March  date. 

Observe  that  1920  is  a  leap  year,  which  gives 
29  days  for  February. 


16.  Find  the  interest  on  $1864  at  6%  (a)  for  7  mo. 
21  da.  (b)  For  235  da. 

Since  360  is  generally  taken  as  the  number  of  days 
to  the  interest  year,  it  would  be  more  reasonable  to 
use  7  mo.  21  da.  as  the  interest  period  on  a  loan  made 
July  25,  1919,  and  paid  March  16,  1920;  but  usage 
generally  permits  the  employment  of  the  number  of 
days  when  the  time  is  less  than  a  year. 

Ascertain  the  practice  prevalent  in  your  neighbor- 
hood. 

In  the  following  examples,  use  the  number  of  days 
between  the  given  dates: 

16.  Find  the  interest  on  $1084  from  Jul.  25,  1919, 
to  March  16,  1920  (a)  at  5%;  (6)  at  6%;  (c)  at  7%; 
(d)  at  8%. 


BUSINESS  CALCULATIONS  99 

METHOD 

(a)  $1084  X  .05  X  235    (b)  $1084  X  .06  X  235 
360  360 

(c)  $1084  X  .07  X  235    (d)  $1084  X  .08  X  235 
360  360 

TEST 

In  making  the  test  by  the  use  of  aliquot  parts, 
do  not  find  the  interest  for  a  year  unnecessarily. 

(a)  5%      (b)  6%         (c)  7%       (d)  8% 
Principal  $1084        $1084          $1084          $1084 
1  yr.  $75.88 

180  da.       $27.10         $32.52         $37.94       $43.36 
45    " 

9    " 
1     " 

235  da.          Ans.  Ans.  Ans.        Ans. 

(a)  The  interest  for  %  yr.  at  5  %  is  2^%  of  the  prin- 
cipal, or  %Q  of  it.     Divide  $1084  by  40. 

(b)  Find  the  interest  for  180  da.  by  taking  3  %  of 
$1084. 

(c)  Write  the  interest  for  a  year,  then  take  %  of  it. 

(d)  Take  4  %  of  $1084  for  the  interest  for  180  da. 


100         WALSH'S  BUSINESS  ARITHMETIC 

17.   Find  the  interest  on: 

a  $1192  at  3%  from  Mar.  10,  1919  to  Jan.    29,  1920 

b  1283  "8%  "  Dec.   30,  1918  "  Mar.  18,  1919 

c  1374  "4%  "  Apr.    20,  1920  "  Sep.    26,  1920 

d  1465  "6%  "  Sep.    12,  1918  "  Jul.     21,  1919 

e  1556  "5%  "  Jul.     16,  1919  "  Apr.    12,  1920 

/  1647  "7%  "  Feb.    23,  1920  "  Jun.    30,  1920 

g  1738  "6%  "  May  29,  1919  "  Mar.  31,  1920 

h  1829  "5%  "  Jun.    15,  1920  "  Aug.  28,  1920 

i  1910  "7%  "  Aug.   14,  1919  "  Jun.    30,  1920 

j  2029  "4%  "  Jan.    18,  1921  "   May  20,  1921 

•k  2138  "8%  "  Mar.  25,  1919  "  Feb.    29,  1920 

/  2247  "7%  "  Dec.    18,  1920  "  Jan.    31,  1921 

m   2356  "9%  "  Apr.    11,  1919  "  Feb.    16,  1920 

n  2408  "3%  "  Sep.    26,  1920  "  May  15,  1921 

PREPARATORY  EXERCISES 

1.  In  finding  the  value  of  the  following  expressions, 
which  product  should  first  be  obtained?     Why? 

a  125  X  5%  X  8         6  300  X  3%  X  S%        c  250  x  6^  X  4 

2.  Wliich  product  should  first  be  found  in  finding 
the  value  of  the  following?    "Why? 

a  4  X  137  X  2%         b  6  X  389  X  %        c  6  X  594  X  1% 

3.  Give  the  value  of  each  of  the  foregoing. 

SIGHT  EXERCISES 
1.   Give  the  interest  on: 

a  $125  at  5%  %  for  8  yr.  b  $300  at  3%  %  for  3%  yr. 

c     250   "  6%%  "   4   "  d     137  "  2^%   "   4     " 

e     389  "  6%     "   X  "  /     594  "  6%      "   1%  " 


BUSINESS  CALCULATIONS  '101 

2.  Give  the  interest  on  $963  at  6%  (a)  for  %  yr. 
(6)  For  2  mo.     (c)  For  60  da. 

3.  Give  the  interest  on  $480  for   (a)   60  da.      (b) 
30  da.     (c)  15  da.    (d)  2  mo.     (e)  I  mo.     (/)  4  mo. 

4.  What  fraction  of  60  days  is: 

a  15  da.?     b  20  da.?     c  45  da.?     d  6  da.?     e  2  da.?    /  4  da.? 
010  da.?     hl2  da.?     i30da.?    j  5  da.?     fc  3  da.?     /Ida.? 

5.  Give  the  interest  on  $540  at  6%  for: 

a  15  da.       b  60  da.       c  20  da.       d  1  da.       e  5  da.      /  3  da. 
0  12  da.       h  10  da.       i  30  da.      j  6  da.       A;  2  da.       Z  4  da. 

6.  What  decimal  of  60  days  is: 

a  54  da.?     b  18  da.?     c  42  da.?     d  36  da.?     e  24  da.? 

7.  Give  the  interest  on  $500  at  6  %  for: 
a  72  da.     b  48  da.     c  66  da. 


METHOD 

a  72  da.  =  1.2  of  60  da.  $5  X  1.2  =  $6,  Ans. 
b  48  "  =  .8  "  "  "  $5  X  .8  =  $4,  Ans. 
c  66  "  =  1.1  "  "  "  $5  X  1.1  =  $5.50,  Ans. 


8.  Give  the  interest  on  $400  at  6 %  for: 

a  54  da.     b  18  da.     c  42  da.     d  36  da.     e  24  da.    /  6  da. 

9.  Give  the  interest  at  6  %  on : 

a  $249  for  60  da.  b  $240  for  5  da. 

c  333  "  20  "  d  420  "  3  " 

e  510  "  12  "  /  670  "  6  " 

g  864  "  30  "  h  660  "  1  " 

i  726  "  10  "  j  450  "  4  " 

k  488  "  15  "  /  690  "  2  " 


102          WALSH'S  BUSINESS  ARITHMETIC 

10.   Using  decimals,  give  the  interest  at  6%  on: 

a  $215  for  24  da.  b  $110  for  54  da. 

c  310   "    66   "  d    210    "  48   " 

e  330   "    18   "  /     120    "  36   " 

g     120  "    42  "  h    300    "  72   " 

60-DAY  METHOD— RATE  6% 

In  calculating  interest  at  6%  for  short  periods, 
business  men  generally  point  off  1%  of  the  principal 
as  the  interest  for  60  days. 

WRITTEN  EXERCISES 

1.  Find  the  interest  on  $583.20  at  6  %  (a)  for  90  da. 
(6)  For  80  da.  (c)  For  75  da.  (d)  For  72  da. 


METHOD 

(a)    60  da.         $5.832         (6)     60  da.        $5.832 
+  30     "  00    2.916  +  20    "   00     1.944 

90  da.  ?  80  da.  ? 

(c)     60  da.        $5.832         (d)    60  da.        $5.832 
+  15    "   00    1.458  +12    "(JO    1.166 

75  da.  ?  72  da.  ~ 

Write  the  interest  for  60  days  by  moving  the 
decimal  point  in  the  principal  two  places  to  the 
left. 

Find  the  interest  for  90  days,  80  days,  75  days, 
and  72  days,  respectively,  by  adding  to  the  interest 
for  60  days  %  of  itself,  %  of  itself,  %  of  itself,  and  % 
of  itself,  respectively. 
Test  results,  using  cancellation  method. 


BUSINESS  CALCULATIONS  103 

2.   Find  the  interest  on  $465.30  at  6%  for  100  da. 


METHOD 

Int.  for  60  da.  $4.653 

"     "  30    "     2.3265     y2  of  60  da. 

"     "JLO    "       .7755     %   "30    " 
Int.  for  100  da.  $7.76     Ans. 
Test  by  taking  60  da.,  20  da.,  and  20  da. 


3.  Find  the  interest  on  $695.40  at  6%  (a)  for  95 
da.  (6)  For  84  da.  (c)  For  78  da.  (d)  For  74  da. 
(e)  For  67  da. 


METHOD 

60  da.        60  da.        60  da.        60  da.        60  da. 
30    "          20    "          15    "          12    "  6    " 

J5    "  4    "  3    "  2    "  1    " 

(a)  95  da.   (6)  84  da.    (c)78da.   (d)74da.   (e)  67  da. 
Test  (6)  by  taking  60  da.,  12  da.,  and  12  da. 


4.  Find  the  interest  at  6  %  on : 

a  $372  for  81  da.     b  $477  for  93  da.     c  $165  for  63  da. 

d    513   "    72    "      e     615   "   84    "      /    723   "   67   " 

5.  What  is  the  interest  on  $394.75  at  6%  for  86 
days? 


104          WALSH'S  BUSINESS  ARITHMETIC 


METHOD 

60  da.  $3.9475  6  days,  while  not  an 

20     "     1.3158  %   of  60  da.    aliquot    part    of    20 

6     "       .3948  Ko    "  60   "      days,    is    an    aliquot 

?  part  of  60  days. 

Be  careful  to  take  Ko  of  $3.9475. 


6.  Using  three  aliquot  parts,  find  the  interest  at 
6%  on: 

a  $684  for  73  da.     b  $495  for  77  da.     c  $783  for  86  da. 

7.  Find  the  interest  on  $834.36  at  6  %  (a)  for  45  da. 
(b)  For  48  da.     (c)  For  50  da.     (d)  For  54  da.     (e) 
For  55  da.     (/)  For  59  da. 


METHOD 

(a) 
60  da 

60  da. 

60  da. 

-  15    " 

-  12    " 

-  10    " 

45  da 

48  da. 

50  da. 

(d) 
60  da 

w 

60  da. 

60  da. 

-    6    " 

-    5    " 

1    " 

54  da 

55  da. 

59  da. 

From  the  interest  for  60  days,  deduct 
as  indicated. 

the  interest 

Test  (b)  by 
by  .8;  test  (d) 

multiplying  the  interest 
by  multiplying  it  by  .9. 

for  60  days 

BUSINESS  CALCULATIONS  105 

8.  Find  the  interest  at  6%  on: 

a  $954  for  58  da.     b  $693  for  57  da.     c  $765  for  56  da. 

9.  Find  the  interest   on   $1232.73   at   6%    (a)    for 
16  da.     (6)  For  33  da.     (c)  For  29  da.     (d)  For  53 
da.     (e)  For  47  da.     (/)  For  44  da. 


METHOD 

60  da.                  60  da  60  da. 

15  da.                  30  da.  30  da. 

+  _1    "              +  _3    "  J_    " 

(a)        16  da.  (6)      33  da.  (c)      29  da. 

60  da.  60  da.  60  da. 

6    "  -  10    "  -  10    " 

1    "  3    "  -_6    " 

(d)       53  da.  (e)       47  da.  (/)     44  da. 

In  (a),  (b),  and  (c),  draw  a  line  under  the  interest 
for  60  days,  excluding  that  portion.  In  (d)  and 
(e),  from  the  interest  for  60  days  deduct,  in  one 
operation,  the  sum  of  the  two  having  a  prefixed 
minus  sign. 


10.   Find  the  interest  at  6  %  on : 

a  $297  for  17  da.     6  $459  for  26  da.     c  $576  for  52  da. 
d    708     "35    "      e     693     "44    "      /    351   "    19   " 


106          WALSH'S  BUSINESS  ARITHMETIC 

11.   Find  the  interest  on  $972  for  87  days  (a)  at  6%; 
(6)  at  5%;   (c)  at  4}£%;   (d)  at  8%. 


Use  1%  of  the  principal  as  the  interest  for  72  days  (^year)  at  5%,  for 
80  days  (%  year)  at  4}£%,  and  for  45  days  (%  year)  at  8%. 


METHOD 

(a)  6%  (6)  5% 

60  da.    $9.72  72  da.    $9.72 

+  15     "       2.43  +  12     "       1.62 

+  12     "       1.944  +    3     "         .405 
87  da.  $14.09  Ans.  87  da.  $11.75  Ans. 


(c)  4^%  (d)  8% 

80  da.  $9.72         45  da.  $9.72 
+  8  "    .972        90  "  19.44 

1  "    .1215  —  3  "    .648 
87  da.  $10.57  Ans.     87  da.  $18.79  Ans. 


12.  Find  the  interest  on  $429  for  97  days  (a)  at  6  %. 
(6)    At  5%.     (c)  At  4#%.     (d)  At  4%.     (e)  At  9%. 

13.  Find  the  amount  of  $972  for  75  days  (a)  at  6%; 
(6)  at  4%;    (c)  at  8%. 


METHOD 

(a)  (6) 

Principal       $972.-  $972.- 

Int.    60  da.  +    9.72  90  da.  +  9.72 

"     15    "  +    2.43  15    "  --1.62 

Amt.  75  da.  $984.15  Ans.  $980.10  Ans. 

For  (c),  take  45  da.,  15  da.,  and  15  da. 


BUSINESS   CALCULATIONS  107 

14.  Find  the  amount  of  $864  for  98  days  (a)  at  5%; 
(b)  at  6%;   (c)  at  4%. 

Some  clerks  begin  with  the  6  %  rate  in  all  interest 
calculations,  making  the  necessary  change  in  this 
result  to  conform  with  the  rate  specified  in  a  given 
transaction. 

15.  Find  the  amount  of  $972  for  66  days  (a)  at  7%; 


Int.  60  da. 

"       6     " 

METHOD 

(a) 
at  6%       $9.72 
+  .972 

Int.  66  da. 

«      «     « 

at  6%     $10.692 

"1%  +    1.782 

Int.  66  da. 
Principal 

at  7%     $12.47 
972.- 

Amount 

Int.  66  da. 

«      ((     « 

<t      «     « 

$984.47  Ans. 

(b) 
at    6%  $10.692 
"  IX  %-  2.673 
"    y*%  -    .4455 

Int.  66  da. 
Principal 

at  4/4%  +$7.57 
972.+ 

Amount 

$979.57  Ans. 

16.   Find  the  interest  using  any  method.  Test  the 
result  by  using  another  method. 

Principal     Rate      Time  Principal     Rate  Time 

a  $306         5  %         66  da.          b  $603         4  %  68  da. 

c     702        8%         83    "  d    801         3%  54    " 


108 


WALSH'S  BUSINESS  ARITHMETIC 


When  you  calculate  interest  by  commencing  with  a 
rate  other  than  the  given  one,  be  careful  to  find 
the  interest  at  the  latter  rate  before  adding  it  to 
the  principal  to  obtain  the  amount. 

17.  Find  the  interest  on  $594  for  100  days  (a)  at 
6%.  From  this  result  determine  the  interest  (b)  at 
5%  %.  (c)  At  6/2  %.  (d)  At  7  %.  (e)  At  7Y2  %. 


METHOD 

(6) 

(c) 

W 

w 

At    6% 

At    6% 

At  6% 

At    6% 

—  %% 

+  %% 

+  1% 

+     1/2% 

M%          W%         7%          7y2% 

18.    Find  the  amount: 
Principal     Rate      Time 


a  $954 
c     648 


5%  % 


49  da. 

73    " 


Principal 
6  $891 
d     765 


Rate 

7  % 
7^% 


Time 
96  da. 

81     " 


19.  A  man  incurred  a  debt  of  $465.30,  which  he 
repaid  in  3  yr.  8  mo.  24  da.  with  interest  at  5  %.  WTiat 
was  his  total  payment? 


SIGHT  EXERCISES 

1.  Give  the  interest  at  6%  on  $360  for  81  days. 

NOTE:  Change  mentally  the  foregoing  as  follows;   Give  the  interest  on 
$81  for  360  days  at  6  %. 

2.  Give  the  interest  on  $360  at: 

a  6  %  for  70  da.  b  4%  %  for  60  da. 

c  5%    "  46    M  d  5%%    "  40    " 

e  4%    "  82    "  /  6^%    "  80    " 


CHAPTER  FOUR 
BANK    DISCOUNT 

William  Me  Wilson  applies  to  his  bank  for  a  loan  of 
$1200  to  buy  cattle  he  wishes  to  fatten.  The  bank 
authorities  agree  to  make  the  loan,  taking  as  security 
his  note  indorsed  by  a  responsible  person. 

The  following  is  the  note: 


Oklahoma,   September  16, 


Mr.  McWilson  makes  out  the  note  to  his  own 
order  thereby  becoming  maker  and  payee.  He  then 
becomes  an  indorser.  Mr.  McWilson  then  delivers 
the  note  to  the  bank  by  writing  his  name  across  the 
back.  To  furnish  the  required  security,  he  obtains 
the  indorsement  of  Mr.  Schwerzel,  which  the  latter 
gives  by  writing  his  name  on  the  back  of  the  note 
under  that  of  Mr.  McWilson. 

109 


110          WALSH'S  BUSINESS  ARITHMETIC 

INDORSEMENT 


fioley,  tokla,.,  &fi.  /6, 

date,,  c/  fo'uymAA,&  to-  'jawy  to-  the, 

Jwncli&cl  °%oo 
at 


DISCOUNTING   THE   NOTE 


The  bank  "discounts"  the  foregoing  note  by  de- 
ducting in  advance  the  interest  from  September  16, 
1919,  to  March  16,  1920,  the  date  the  note  is  due. 

From  the  date  table  the  bank  cashier  finds  the  time  to 
be  182  days;  from  the  interest  table  he  finds  the  interest 
(bank  discount)  to  be  $36.40.  Deducting  the  latter  from 
$1200  (the  face  of  the  note)  he  credits  Mr.  Me  Wilson's 
account  with  the  remainder,  $1163.60  (the  proceeds). 


PROCEEDS  =  Face  of  Note  -  Bank  Discount 


WTien  the  note  becomes  due,  March  16,  1920,  the 
bank  deducts  $1200  from  Mr.  Me  Wilson's  account  and 
places  the  note  with  his  canceled  checks,  to  be  returned 
to  him  with  the  latter  at  the  proper  time. 


To  find  the  BANK  DISCOUNT  on  a  non-interest  bearing 
note,  find  the  interest  on  the  face  of  the  note  from  the  day 
of  discount  to  the  day  of  maturity. 


BUSINESS  CALCULATIONS  111 

SIGHT  EXERCISES 

1.  What  is  the  interest  on  $1000  at  6  %  for  60  days? 

2.  What  is  the  interest  on  a  60-day  loan  of  $1000, 
at6%? 

3.  If  the  interest  is  paid  in  advance  by  the  borrower, 
how  much  remains  for  his  use? 

4.  What  is  the  bank  discount  on  $1000  for  60  days 
at6%? 

5.  What  are  the  proceeds  of  a  note  for  $1000  dis- 
counted at  a  bank  for  60  days  at  6%? 

6.  Give  the  bank  discount  (interest)  at  6%  on  a 
note  of  $1200  for: 

a    60  da.  b  30  da.  c    6  da.  d  120  da. 

e    10    "  /   15   "  01"  h  180   " 

i    24    "  j   12  "  k  5    "  /   240  " 

m  66    "  n  54   "  o   9    "  p  300   " 

q    18    "  r   36   "  52"  t  150    " 

u   42    "  0  48   "  w  7    "  x  210   " 


7.   Give  the  proceeds  of  a  note  for  $1200,  discounted 
at  a  bank  at  6  %  for : 

a    30  da.  b  60  da.  c    3  da.  d  240  da. 

e    90    "  /  24   "  g    6    "  h  120  " 

i    15    "  j   36   "  k  9    "  Z    180  " 


WRITTEN  EXERCISES 

1.  What  is  the  bank  discount  of  a  note  for  $475.20 
discounted  at  a  bank  at  6%  for  (a)  48  da.?  (b)  For 
72  da.? 


112          WALSH'S  BUSINESS  ARITHMETIC 


PROCESS 

Face  of  note   (a)  $475.20  (6)    $475.20 


Int.  for  60  da.  $4.752          60  da.      $4.752 

"     "     12"  -  .9504    +12   "  .9504 

Ans.      $3.80  Ans.      $5.70 


2.  Find  the  bank  discount  at  6  %  on  notes  as  follows : 

Face  Discount  Face  Discount 

of  Note  Period  of  Note "  Period 

a  $443.89  108  da.  b  $367.64  98  da. 

c     855.78  119    "  d  665.73  66    " 

e     627.39  164    "  /  122.58  32    " 

g     435.87  100    "  h  146.52  58    " 

i     625.34  105    "  j  346.53  65     " 

k    837.25  102    "  /  635.89  97    " 

3.  Find  the  proceeds  of  a  note  for  $378,  discounted 
at  a  bank  at  6  %  (a)  for  63  days,     (b)  For  57  days. 


METHOD 


(a)     $378.  -      Face  of  note 
Int.  for  60  da.    -  3.78 

«     -     3     " 


Ans.     $374.03 

(b)    $378.  -     Face  of  note 
Int.  for  30  da.        1.89 
"      "  27     "         1.701 
Ans.     $374.41 

In  (b)  find  the  interest  for  27  days  by  multiplying 
$1.89,  the  interest  for  30  days,  by  .9. 


BUSINESS  CALCULATIONS 


113 


4.   Find  the  proceeds  of  the  following  notes  dis- 


counted at  6  % 

Face 
of  Note 
a  $657.83 
868.35 
285.72 
432.12 
524.63 
774.34 


Discount 
Period 
112  da. 
108 
130 
107 
101 
123 


Face 

Discount 

of  Note 

Period 

b  $796.52 

64  da. 

d    473.76 

37    " 

/     985.31 

59    " 

h    523.46 

38    " 

j     418.52 

67    " 

/     293.75 

94    " 

DAYS   OF   GRACE  —  HOLIDAYS 


When  the  day  on  which  a  note  by  its  terms  is  made 
payable  (date  of  maturity)  is  a  Sunday  or  a  holiday, 
the  laws  of  many  states  defer  its  maturity  to  the 
following  business  day.  In  a  state  in  which  Saturday 
is  a  half -holiday,  a  note  falling  due  on  Saturday  does 
not  mature  until  Monday;  or,  when  Monday  is  a 
holiday,  until  Tuesday. 

Thus  a  note  for  30  days,  drawn  June  3,  is  due  July  3. 
When  this  falls  on  Saturday  (as  in  1920)  the  note 
runs  for  33  days.  In  discounting  the  note,  the  bank 
takes  note  of  these  conditions  and  deducts  interest 
for  33  days,  the  term  of  discount. 

In  some  states  an  allowance  of  three  days,  called 
days  of  grace,  is  given  after  the  note  is  due  in  accord- 
ance with  its  terms.  These  days  are  taken  into 
consideration  by  the  bank  in  determining  the  discount 
period  in  states  in  which  days  of  grace  prevail. 

While  the  pupil  should  familiarize  himself  with  the 
practice  of  the  neighborhood,  he  may  ignore  in  the 
following  examples  the  matter  of  holidays,  days  of 


114          WALSH'S  BUSINESS  ARITHMETIC 

grace,  etc.,  and  assume  that  the  note  is  payable  on 
the  day  specified  by  its  terms  for  its  maturity. 

DATE  OF  THE  MATURITY  OF  A  NOTE 

A  note  for  30,  60,  90,  etc.,  days,  is  payable  30,  60, 
90,  etc.,  days  after  its  date:  that  is,  a  note  for  30  days 
dated  February  17,  1919,  is  due  March  19,  1919, 
and  one  dated  February  17,  1920,  is  due  March  18, 
1920. 

A  note  for  30  days  has  30  days  to  run;  a  note  for 
1  month  may  be  payable  in  28  days,  29  days,  30  days, 
or  31  days. 

A  note  for  1  month  dated  January  31,  1919,  is  pay- 
able February  28,  1919,  28  days;  one  dated  January 
31,  1920,  is  payable  February  29,  1920,  29  days;  a 
note  for  1  month  dated  January  28  is  payable  February 
28,  31  days;  one  dated  June  25  is  payable  July  25, 
30  days. 

The  expressions  that  a  note  is  "drawn,"  "made," 
or  "dated,"  on  a  specified  day,  have  the  same  mean- 
ing. 

SIGHT  EXERCISES 

1.  Give  the  date  when  each  of  the  following  notes 
becomes  due: 

Drawn  Time  Drawn  Time 

a   Jan.   30,  1921  1  mo.  b  May  31,  1919  1  mo. 

c    Oct.    13,  1920  30  da.  d  Feb.  23,  1921  30  da. 

e    Jul.    31,  1919  2  mo.  /  Dec.  30,  1919  2  mo. 

g    Feb.  18,  1920  60  da.  h  Feb.  16,  1921  60  da. 

i    Nov.  30,  1919  3  mo.  j   Sep.  30,  1920  3  mo. 

k    Jan.   31,  1920  90  da.  I    Aug.  15,  1919  90  da. 

m  Mch.  16,  1919  4  da.  n  Feb.  29,  1920  4  mo. 


BUSINESS  CALCULATIONS  115 

2.  Give  the  number  of  days  between  the  date  on 
which  each  of  the  following  notes  is  drawn,  and  the 
date  on  which  it  falls  due: 

Drawn  Time                        Drawn  Time 

a    Jan.   30,  1921  1  mo.  6  May  31,  1919        1  mo. 

c    Jul.    31,  1919  2  mo.  d  Dec.  30,  1919         2  mo. 

e    Nov.  30,  1920  3  mo.  /  Feb.  16,  1921         3  mo. 

g    Mch.  16,  1919  4  mo.  h  Apr.  30,  1920         4  mo. 

BANK  DISCOUNT   OF   COMMERCIAL  PAPER 

J.  R,  Page  &  Co.  buy  machinery  for  $4000,  giving 
in  payment  a  note  for  4  months,  in  the  following  form : 


Ashland,  Ore.,  October  31,  1919 
Four  months  after  date,  we  promise  to  pay 
to  the  order  of  the  Lidgewood  Mfg.  Co. 

Four  Thousand  00/100 Dollars 

Value  Received,  at  the  United  States  National  Bank. 
$400%o  J.  R.  Page  &  Co. 


The  firm  mails  this  note  to  the  Denver  Office  of  the 
Lidgewood  Mfg.  Co.  On  November  4  the  latter  has 
the  note  discounted  at  the  Colorado  National  Bank. 

SIGHT  EXERCISES 

1.  (a)  On  what   day  is   the  foregoing   note   due? 
(6)  How  many  days  after  October  31? 

2.  (a)  How  many  days  after  it  was  drawn  was  it 
discounted?     (6)  How  many  days  are  there  from  the 
day  of  discount  to  the  day  it  is  due?     (c)  What  is  the 
interest  on  $4000  at  6%  for  this  latter  period? 


116          WALSH'S  BUSINESS  ARITHMETIC 

3.  On  December  6,  the  Colorado  National  Bank 
"sells"  this  note  to  the  Mississippi  Trust  Co.,  of  St. 
Louis;  that  is,  the  latter  discounts  the  note  for  the 
remainder  of  the  term,  (a)  How  many  days  was  the 
note  held  by  the  Colorado  National  Bank?  (b)  How 
much  interest  did  it  earn  in  that  time  at  6%?  (c) 
How  many  days  will  elapse  from  December  16,  1919 
to  the  maturity  of  the  note?  (d)  What  is  the  bank 
discount  on  $4000  at  5%  for  this  period? 

NOTE:  Bank  Discount  and  Interest  have  the  same  meaning. 
TERM   OF  DISCOUNT 

In  many  discount  examples  the  period  (term  of 
discount)  for  which  the  discounting  bank  deducts 
interest  is  not  specified.  When  money  is  borrowed 
from  a  bank  on  a  note,  the  latter  is  generally  dis- 
counted on  the  day  it  is  drawn,  and  the  discount 
(interest)  period  corresponds  with  the  time  specified 
in  the  note.  When  this  is  stated  in  days,  30  days, 
60  days,  etc.,  the  interest  is  taken  for  the  specified  num- 
ber (omitting  from  consideration  the  question  of 
holidays).  WTien  the  time  is  expressed  in  months, 
3  months,  6  months,  etc.,  the  number  of  days  must 
be  ascertained. 

WRITTEN  EXERCISES 

1.  Calculate  (a)  the  bank  discount  and  (b)  the 
proceeds  of  a  note  for  $864,  for  4  months,  drawn 
Dec.  31,  1920,  and  discounted  at  5%  on  the  same 
day. 


BUSINESS  CALCULATIONS  117 


METHOD 

Find  the  date  of  maturity,  4  months  after 
Dec.  31,  1920,  viz.,  Apr.  30,  1920. 

The  time  between  those  dates  is  31  da.  +  28  da. 
+  31  da. +  30  da. 

Obtain  (a)  by  finding  the  interest  for  the  fore- 
going time. 

Test. 


2.  Calculate  the  bank  discount  on  the  following 
notes,  discounted  at  6%  on  the  day  drawn. 

Face  Drawn  Time 

a  $396.90  May  23,  1919  2  months 

b     487.45  Oct.  31,  1920  4       " 

c     543.60  Jan.  20,  1921  6       " 

d     627.15  Jul.    16,  1920  3       " 

DATE   OF  DISCOUNT 

When  a  note  is  given  in  settlement  of  a  business 
transaction,  it  may  not  be  discounted  for  several 
days.  In  working  examples  of  this  kind,  the  care- 
less pupil  may  make  an  error  in  the  discount  period. 
Among  the  data  he  finds  that  a  note  was  made  on 
March  31  and  discounted  May  13.  Ignoring  the  item 
which  states  that  the  note  was  drawn  for  90  days,  or 
for  4  months,  etc.,  he  takes  as  the  discount  period  the 
43  days  between  the  foregoing  dates.  This  is  the 
time  for  which  interest  is  not  deducted.  The  dis- 
count period  begins  May  13  and  terminates  on  the 
day  the  note  is  due.  The  March  31  date  is  used  only 
as  the  basis  for  the  determination  of  the  date  of  maturity. 


118          WALSH'S  BUSINESS  ARITHMETIC 

SIGHT  EXERCISES 

1.  A  60-day  note  is  discounted  12  days  after  it  is 
drawn.     What  is  the  term  of  discount? 

2.  Give  the  term  of  discount  of  each  of  the  following: 

Time  Discounted 

a  60  da.  15  days  after  date 
b  30     "  9       " 

c  90     "  32      "         "       " 

d  80     "  56       "         "       " 

3.  Give  the  term  of  discount: 

Time  Dated  Discounted 

a  60  da.  Jan.    13  Jan.  31 

b  30     "  Feb.  10  Feb.  28 

c  90     "  Mar.  25  Apr.  10 

d  80     "  Apr.   16  Apr.  30 

WRITTEN  EXERCISES 

1.  Calculate  the  proceeds  of  the  following  notes: 

Face  Discounted  Rate 

a  $783.90  48  days  before  maturity  6  % 

b     842.76  63      "  "  5% 

c     927.54  75      "  "  8% 

d    648.36  87      "         "  "  7%' 

X 

2.  Calculate  the  discount  on  the  following  notes: 

Face  Drawn  for  Discounted  Rate 

a  $567  90  da.  25  days  after  date  6%% 

b     732  30  "  12      "  6% 

c     984  60  "  15       "  5^% 

d     652  80  "  42      "         "       "  7% 


BUSINESS  CALCULATIONS  119 

3.  Calculate  the  bank  discount  on  a  note  of  $1236 
drawn  Feb.  18,  1920,  for  90  days  and  discounted  at 
5  %,  Apr.  13,  1920. 


METHOD 

To  find  the  term  of  discount  in  this  case,  it  is 
not  necessary  to  determine  the  date  of  maturity. 
From  Feb.  18,  1920  to  Apr.  13,  1920  the  time  is 
11  da.  +  31  da.  +  13  da.,  or  55  days,  which  is  the 
period  the  note  has  been  withheld  from  discount. 
The  remaining  time,  35  days  (90  days  —  55  days), 
is  the  time  during  which  the  borrower  has  the  use 
of  the  bank's  money,  and  the  period  for  which  he 
must  pay  interest. 


4.   Calculate  the  bank  discount  on  the  following 
notes : 


Face 

Time 

Dated 

Discounted 

a  $1350 
6  2880 
c  3240 
d  4320 

90  da. 

80  " 
60  " 
70  " 

Jan.  5,  1918 
Dec.  6,  1919 
Jul.  7,  1920 
Sep.  6,  1921 

Mar.  4,  1918 
Feb.  8,  1920 
Jul.  9,  1920 
Oct.  1,  1921 

5.  A  note  for  $1560  drawn  Oct.  31,  1920,  for  4 
months,  was  discounted  Dec.  5,  1920,  at  5%%.  Find 
(a)  the  day  the  note  is  due;  (b)  the  term  of  discount; 
(c)  the  discount. 


120          WALSH'S  BUSINESS  ARITHMETIC 


METHOD 

(a)  The  note  is  due  4  months  after  Oct.  31,  1920, 
which  is  Feb.  28,  1921. 

(6)  The  term  of  discount  is  the  number  of  days 
between  the  day  of  discount,  Dec.  5,  1920,  and 
the  day  the  note  is  due,  Feb.  28,  1921. 


Observe  that  a  note  for  4  months  drawn  on  Oct.  28,  Oct.  29,  Oct.  30, 
or  Oct.  31,  1920,  is  due  on  Feb.  28,  1921. 

6.  Find  (I)  the  date  on  which  each  of  the  follow- 
ing notes  is  due;  (II)  the  discount  period;  (III)  the 
bank  discount;  and  (IV)  the  proceeds. 


Face 

Time 

Dated 

Discounted 

Rate 

a  $1080 

3  mo. 

Feb.  16,  1918 

Feb.  28,  1918 

5% 

b    3240 

6    " 

Jun.  28,  1919 

Nov.  15,  1919 

6% 

c    2560 
d    4440 

2    " 
4    " 

Sep.  15,  1920 
Jul.   30,  1921 

Sep.  30,  1920 
Aug.  10,  1921 

6% 

5% 

DISCOUNT   OF  INTEREST-BEARING  NOTES 

As  evidence  of  a  loan  to  Percy  Keating,  Lester 
Johnson  received  the  following  note: 

SHELDON,  N.  DAK.,  March  6,  1920 
Ninety  days  after  date  I  promise  to  pay  to  the  order  of 

Lester  Johnson 
Twelve  Hundred  00/100  .................................    Dollars 

Value  received,  with  interest  at  5  %. 

$1200%,  Percy  Keating 

Mr.  Johnson  loaned  this  money  at  a  time  he  thought 
he  would  not  need  it  for  ninety  days,  and  he  was  glad 
of  the  opportunity  to  lend  it  at  a  fair  rate  of  interest. 


BUSINESS  CALCULATIONS 

The  need  for  cash  before  the  maturity  of  the  note 
made  it  necessary  for  him  to  offer  it  to  his  bank  as 
security  for  a  loan.  The  bank  agreed  to  discount  the 
note  at  6%  on  the  amount  of  the  note  at  maturity. 
On  Apr.  5  Mr.  Johnson  transferred  the  note  to  the 
bank  by  indorsement,  thereby  agreeing  to  pay  it  on 
the  failure  of  Mr.  Keating  to  "take  it  up"  at  its 
maturity.  On  Apr.  5  the  bank  discounted  the  note 
at  6%  and  placed  the  proceeds  to  the  credit  of  Mr. 
Johnson. 

SIGHT  EXERCISES 

1.  On  what  date  is  the  foregoing  note  due? 

2.  (a)  What  is  the  interest  on  $1200  at  5%  for  % 
year?     (6)  What  is  the  amount  of  the  note    at   its 
maturity? 

3.  (a)  How  many  days  are  there  between  Apr.  5 
and  the  maturity  of  the  note?     (6)  What  is  the  bank 
discount  at  6%  for  this  time  on  the  amount  of  the  note 
at  maturity?     (c)  How  much  does  the  bank  place  to 
the  credit  of  Mr.  Johnson? 

In  discounting  a  note,  the  bank  authorities  calculate 
the  bank  discount  on  the  sum  the  maker  agrees  to 
pay  at  its  maturity.  In  the  case  of  a  note  that  does 
not  call  for  the  payment  of  interest,  this  corresponds 
with  its  "face."  When  the  note  provides  for  the 
payment  of  interest,  the  sum  to  be  paid  at  its  maturity 
must  be  determined.  This  is  the  "amount"  of  the 
specified  sum,  which  includes  the  "face  of  the  note" 
plus  the  interest. 

The  note  Mr.  Johnson  offers  for  discount  calls  for 


122          WALSH'S  BUSINESS  ARITHMETIC 

the  payment  of  $1200  +  $15  on  Jun.  5,  a  total  of 
$1215.  The  bank  discount  is  the  interest  at  6% 
on  $1215  from  Apr.  6  to  Jun.  5. 

WRITTEN   EXERCISES 

1.  Determine  the  proceeds  of  a  note  for  $1200, 
dated  Jan.  9,  1922,  payable  in  60  days,  with  interest 
at  6%,  and  discounted  at  a  bank  on  Feb.  1,  1922, 
at  6%. 


METHOD 

I.   Find   the   amount   of   $1200   at   6%   for   GO 

days. 
II.    Find  the  date  of  the  maturity  of  the  note. 

III.  Find  the  time  between  Feb.  1  and  the  date 
of  maturity. 

IV.  Find  the  interest  for  this  period  on  the  amount 
obtained  in  I. 

V.   From  I  (the  amount  of  the  note  at  maturity) 
deduct  IV  (the  bank  discount). 


2.   Find  the  proceeds  of  the  following  notes,  which 
bear  interest  at  6%  and  are  discounted  at  6%: 

Face  Time  Dated  Discounted 

a  $1200  90  da.  Jul.    3,  1921  Aug.  16,  1921 

b     2400  60  da.  Jan.  8,  1921  Feb.  25,  1921 

c     3600  30  da.  Jun.  1,  1920  Jun.   15,  1920 


SECTION  III 
NUMBERS  AND  PROCESSES 

CHAPTER  ONE 

READING    AND    WRITING    NUMBERS 
ORAL  EXERCISES 

1.  Read  the  following  numbers:    18,  47,  94,  33,  56, 
69. 

2.  Read    365.     Say    "Three    hundred    sixty-five." 
Do  not  use   "and"  in  reading  an  integer   (a  whole 
number). 

3.  Read  the  following  numbers:   390,  418,  962,  804, 
700. 

4.  Read  4063.    Say  "Four  thousand,  sixty  three." 

5.  Read  the  following  numbers:    9000,  8007,  6052, 
7329,  4010. 

6.  Read   the   following   numbers:     49,000,   38,007, 
26,052,  17,329,  349,000,  238,007,  126,052,  817,329. 

7.  Read,  1,234,000.     Say  "  1  million,  234  thousand." 

8.  Read  the  following  numbers: 

1,249,000  3,238,007  5,126,052 

21,349,000  43,238,007  75,126,052 

321,249,000  543,238,007  675,126,052 

9.  Read   1,234,567,890.     For  convenience  in  read- 
ing a  large    number,   it  is  generally  pointed  off  by 
commas,  into  periods  of  three  figures  each,  beginning 
at  the  right. 

123 


124          WALSH'S  BUSINESS  ARITHMETIC 

The  names  of  the  periods  in  the  foregoing  number 
are  shown  in  the  following: 

TABLE 

BILLIONS'  MILLIONS'  THOUSANDS'  ONES' 

period  period  period  period 


BBS  g  13  § 

1,  234,  667,  890 

Say,  "1  billion,  234  million,  567  thousand,  890." 
Beginning  at  the  left,  announce  the  numbers  repre- 
sented by  the  figures  of  each  period  and  its  name, 
omitting  the  name  of  the  ones'  period. 

10.  Read    1,000,000,890.     Omit    the    name    of    a 
period  composed  exclusively  of  ciphers;    say  "1  bil- 
lion, 890." 

11.  Read  the   following   numbers:    21,000,203,890; 
42,363,000,890;    157,363,275,000. 

Say,  "21  billion,  203  thousand,  890";  "42  billion, 
363  million,  890";  "157  billion,  363  million,  275 
thousand." 

12.  Read  the  following  numbers: 


20,006,854 
3,059,608 
875,340 
51,209,007 

103,050,000 
234,567 
18,620,100 
3,210,001 

1,006,000,053 
2,030,405,000 
28,306,500 
493,062,009 

13.   Read  1200. 

In  the  mental  addition  of  7  hundred  and  5  hundred, 
or  in  the  multiplication  of  4  hundred  by  3,  think  of 
the  result  as  12  hundred. 


NUMBERS  AND  PROCESSES  125 

14.  Read  the  following  numbers  as  hundreds:   1600, 
2100,  3600,  4200,  9800. 

15.  Read  1286. 

In  adding  722  and  564,  think  of  these  numbers  as 
"seven,  twenty -two"  and  "five,  sixty -four,"  respec- 
tively; and  of  the  result  as  "twelve,  eighty -six."  Do 
the  same  in  multiplying  643  by  2,  etc. 

16.  Read  the  following  numbers:   1920,  1776,  1492, 

1898,  1917. 

WRITING   INTEGERS 

1.  Write  one  hundred  two  billion,  seventy-five. 
Remember  that  the  billions'  period  is  the  fourth,  and 

that  it  must  be  followed  by  three  periods  of  three 
figures  each.  Use  three  ciphers  to  represent  the  mis- 
sing millions'  period,  and  three  to  represent  the  missing 
thousands'  period.  Write  a  cipher  in  the  tens' 
place  in  the  billions'  period  and  another  in  the  hun- 
dreds' place  of  the  ones'  period.  Separate  the  periods 
by  commas. 

102,000,000,075 

NOTE:  In  the  European  countries  that  use  a  comma  as  a  decimal  point, 
the  periods  are  separated  by  a  slight  space:  102  000  000  075. 

2.  Write  the  following  numbers: 

One  billion,  eleven  thousand,  seventeen 

Sixteen  hundred  thousand 

Fourteen,  nine- two 

Three  million,  two  thousand,  eighty 

Twenty-four  million,  five  thousand 

Further  practice  will  be  obtained  through  the  writing  of 
numbers  dictated  in  the  addition  exercises. 

NOTE:  Do  not  use  a  comma  in  writing  a  number  of  four  figures,  1890, 
for  example,  unless  such  number  is  written  in  a  column  with  larger  numbers. 


126          WALSH'S  BUSINESS  ARITHMETIC 

DECIMALS 

A  number  preceded  by  a  decimal  point  (.)  is  called 
a  decimal;  .06,  .2,  .135,  for  example. 

The  number  123.45  is  called  a  mixed  decimal.  It 
consists  of  the  integer  123,  and  the  decimal  .45. 


ONE   WAY   OF   READING  DECIMALS 

To  read  333.333,  say  "three  hundred  thirty-three 
and  three  hundred  thirty-three  thousandths,  using 
"and"  between  the  whole  number  and  the  decimal. 

.5  is  a  one-place  decimal;   read  it  as  tenths. 

.15  .05,  etc.,  are  two-place  decimals;  read  them  as 
hundredths.  .157,  .036,  .009,  etc.,  are  three-place 
decimals;  read  them  as  thousandths. 

Read  a  four-place  decimal  as  ten-thousandths,  a 
five-place  decimal  as  hundred-thousandths,  etc. 

To  read  1256.02076,  say,  "1256  and  2076  hundred- 
thousandths."  Read  each  part  in  the  usual  way; 
follow  the  integer  with  the  word  "and,"  and  the  deci- 
mal with  the  denomination  of  its  right-hand  figure. 

TABLE 


NUMBERS  AND  PROCESSES  127 

ORAL  EXERCISE 

Read  the  following: 

217.3  21.073  .0073  12.45 

.058  654.6  1.0271  .00008 

3.02  83.05  350.02  296.4 

THE  BUSINESS  WAY 

1.  Read    the   following:     (a)    700.007     (6)    217.3, 
(c)  .0073,   (d)  12.45 

When  (a)  is  dictated  as  700  and  7  thousandths  to  a  clerk  who  does  not 
know  that  "and"  is  used  to  indicate  a  decimal  point,  he  may  write  it  .707. 

The  business  way  of  stating  this  mixed  decimal,  "Seven  hundred,  point, 
o.o.  seven,"  leaves  no  doubt  in  the  mind  of  the  hearer.  It  is  a  help  to  a 
clerk  who  is  taking  down  a  column  from  dictation  to  begin  to  write  the 
decimal  without  waiting  to  hear  its  denomination. 

Read  the  integer  in  the  usual  way;  say  "point"  to  denote  ^that  what 
follows  is  a  decimal;  announce  separately  each  figure  of  the  latter,  using 
the  letter  "o"  to  denote  a  cipher. 

(6)  Say  "217,  point,  3."  (c)  Say  "Point,  o,  o,  7,  3."  (d)  Say  "12, 
point,  4,  5." 

2.  Read  the  following  in  the  business  way: 

3.5  12.07  6.009  15.038  .005  30.015  .0105  231.25  127 
.0356  213.4  6.8702  375.0006  300.003  12856.02  1856.035 
2963.12  8345.0012  23,589.064  357.00007  1363.0087 
89,362.0501  58,632.001  120,615.838  39,825.36  28,345.0003 

NOTE:  In  some  Continental  countries  the  comma  is  used  as  a  decimal 
point,  a  period  indicating  multiplication.  Observe  that  the  period  used  in 
writing  7.05  A.M.,  for  example,  is  not  a  decimal  point. 

WRITING  DECIMALS 

1.   Write  as  decimals: 

a  143  and  16  ten  thousandths 

b  375  millionths 

c  14,683  and  14,683  hundred  thousandths 


128          WALSH'S  BUSINESS  ARITHMETIC 

Write  (a)  143.0016,  prefixing  two  ciphers  to  the  decimal 
portion  to  indicate  ten-thousandths. 

Write  (6)  .000375  to  make  millionths,  which  denotes  a 
decimal  of  six  places. 

Write  (c)  14,683.14683.  Do  not  use  a  comma  in  the  deci- 
mal portion  to  divide  it  into  periods. 

2.  Write  the  following  decimals: 

a  128  and  75  thousandths 

b  643  millionths 

c  3  and  209  hundred-thousandths 

d  489  and  6  hundredths 

e  25,394  and  1087  ten-thousandths 

/  3  and  96  hundred-thousandths 

g  286  and  3  tenths 

h  57  and  395  ten-thousandths 

i  283  thousandths 

3.  Find  the  sum  of  the  foregoing. 

4.  Write  the  following: 

a  237,  point,  1,0,6 
b  1354,  point,  0,0,7,3 
c  26,903,  point,  0,5,0,9 
d  387,  point,  0,0,0,5 
e  29,  point,  0,0,3,0,1 

5.  Find  the  sum  of  the  foregoing. 

A  person  dictating  numbers  in  a  business  house  omits  the  words  "hun- 
dred" and  "thousand"  when  the  omission  is  not  likely  to  lead  to  misun- 
derstanding. 237  he  announces  as  "two,  thirty-seven";  1354  as  "thirteen, 
fifty-four";  26,903  as  "twenty-six,  9,  0,  3";  etc. 

6.  Write  the  following  from  dictation: 

a  37,  point,  3,0,5 

b  13,  54,  point,  0,0,0,19 

c  26,  nine,  0,  3,  point,  2,0,7,5 

d  18,  3,  75,  point,  6 

e  2,  45,  8,  96,  point,  3 


NUMBERS  AND   PROCESSES  129 

7.   Find  the  sum  of  the  foregoing. 

READING  DOLLARS  AND  CENTS 

The  coin  value  of  a  pound  sterling,  $4,8665,  may  be  read 
.as  4  dollars,  86  cents,  6  mills,  and  5  tenths;  or  as  4  dollars, 
86  cents,  and  65  hundredths. 

The  coin  value  of  a  German  mark  is  23.8  cents.  It  may 
be  read  as  23  cents,  8  mills;  or  as  23  and  8  tenths  cents. 

The  business  man  might  state  the  value  of  a  pound  ster- 
ling as  "4,  point,  8,  6,  6,  5  dollars";  no  one  would  call  it 
4  dollars  and  eight  thousand,  six  hundred  sixty-five  thou- 
sandths of  a  dollar. 

The  word  "and"  is  frequently  omitted  between  the 
number  of  the  dollars  and  that  of  the  cents. 

DICTATING   DOLLARS   AND   CENTS 

In  the  counting  room  it  is  the  duty  of  a  clerk  frequently 
to  call  off  hundreds  of  items  in  dollars  and  cents  to  another 
clerk,  who  then  writes  them  in  columns  to  be  added. 

The  speed  with  which  the  writing  must  be  done  makes 
it  advisable  for  the  "caller-off "  to  omit  everything  unneces- 
sary, but  at  the  same  time  to  be  careful  to  announce  every- 
thing essential. 

$129.36  In    calling    off    the    accompanying 

4375.84  items,  he  should  say:   "One  twenty- 

9. —  nine,    thirty-six.     Forty-three    sev- 

600.75  enty-five,  eighty-four.    Nine  *  dolls.' 

12,308.09  Six  hundred,  seventy-five.     Twelve, 

3,  0,  8,  0,  9. 

It  is  unnecessary  to  employ  the  word  "dollars"  between 
dollars  and  cents,  it  being  sufficient  to  use  it  when  the  item 
does  not  contain  cents,  in  which  case  the  final  syllable  is 
dropped  to  save  every  possible  second. 

When  it  is  agreed  that  the  last  two  figures  represent  cents, 
there  is  no  need  in  calling  off  $600.75  as  "Six  hundred  dol- 


130          WALSH'S  BUSINESS  ARITHMETIC 

lars,  seventy-five."  Announced  as  it  should  be,  with  the 
omission  of  the  word  "dollars, "  it  cannot  be  misunderstood. 
The  "caller-off "  must,  however,  follow  the  wishes  of  the 
transcribing  clerk,  who  is  the  one  held  accountable  for 
errors  in  the  written  numbers. 


WRITING  UNITED   STATES  MONEY 

Fifty-nine  cents  may  be  expressed  with  the  cents' 
sign,  59^;  as  a  fraction  of  a  dollar,  $59/100;  or  as 
a  decimal  of  a  dollar,  $.59,  or  $0.59. 

Three  dollars  and  seventy-five  cents  is  expressed 
twice  in  a  check,  draft,  note,  etc.,  once  as  "Three 
%o  Dollars,"  and  again  as  $37%oo,  the  cents  being 
invariably  written  in  both  places  as  a  fraction  of  a 
dollar.  In  other  connections,  the  form  is  generally 
$3.75,  the  cents  being  written  as  a  decimal  of  a  dollar. 

^'hen  a  number  contains  mills,  it  may  be  written  as 
a  three-place  decimal  of  a  dollar,  or  as  a  decimal  or 
a  fraction  of  a  cent.  Thus,  19  cents  and  3  mills,  the 
coin  value  of  a  French  franc,  is  written  $.193,  or  19.3^, 
or  19%0  cents. 

ORAL  EXERCISES 

Read  the  following  as  you  would  to  a  fellow  clerk: 

a  $81.57  b  $9,104.13  c  $15,836.— 

123.05  360.10  500.95 

47.—  41,235.—  1,206.07 

60.50  300.40  .88 

302.64  .95  423.92 

1249.01  59.84  68.01 

13,100.90  310.25  135  — 

.89  1,606.20  9.96 


NUMBERS  AND   PROCESSES  131 

d  $200.60  e  $384.92     /  $23,456.— 

89.84  1,560.47  6,989.77 

1,603.06  29,879.53  584.18 

172.16  8,808.08  35.45 

399.80  766.67  906.50 

43.-  1,493.—  1,348.— 

21,065.09  35,268.45  854.49 

.63  432.96  2,036.54 

WRITTEN  EXERCISES 

1.  Write  the  foregoing  from  dictation. 

2.  Find  the  sum  of  each. 

READING  FRACTIONS 

To  read  %,  %,  read  the  numerator  as  a  cardinal  num- 
ber, and  the  denominator  as  an  ordinal  number;  to  read 
34%,  use  "and"  between  the  integer  and  the  fraction. 

The  listener  is  sometimes  misled  when  he  hears  such 
an  expression  as  "seven  hundred  and  seventy-nine 
thousandths."  Having  been  taught  that  "and"  in- 
dicates a  mixed  decimal  or  a  mixed  fraction,  he  takes 
the  expression  to  mean  700  7%ooo-  He  does  not  know 
that  the  speaker,  like  many  other  people,  is  unaware 
of  the  existence  of  such  a  rule.  If  he  did,  he  might 
be  undecided  between  77K0oo,  and  77%ooo- 

To  avoid  misunderstandings,  700%oo  should  be 
announced  as  "700  and  the  fraction  %oo";  m/mo 
as  "numerator  779,  denominator  1000." 

g3/ 

Read  a  complex  fraction,  — ,  for  instance,  as  "2% 

9% 

over  3%."  This  form  better  indicates  that  a  fraction  is 
meant  than  "2%  divided  by  3&"  which  may  indicate 
to  the  hearer  the  form  "2%  ^  S£" 


132          WALSH'S  BUSINESS  ARITHMETIC 

ORAL  EXERCISES 
Read  the  following: 

m/s  300%  300%ooo  mAm 

300%oo  3%oo  3%oo  360Kooo 

W  3K  «X  4^ 

2/4  4/2  3%  7^ 

WRITING  FRACTIONS 

In  making  out  bills,  accounts,  etc.,  bookkeepers 
omit  the  denominator  in  writing  a  mixed  number  con- 
taining %,  /2,  %.  They  write  2%,  3&  4%,  respectively, 
as  21,  32,  43,  omitting  the  denominator  (4)  and  the 
line  above  it. 

SIGHT  EXERCISES 

Give  sums: 

a  12l  b  362  c  433  d  842 

6  52  71  33 

2T3  101  6  161 


82  23  82  52 

READING  PER  CENTS 

The  expressions  %%  %%,  and  the  like,  are  frequently 
stated  as  %  of  1  %,  %  of  1  %,  etc.,  to  emphasize  the  fact  that 
each  is  a  fraction  of  a  per  cent. 

WRITING  PER  CENTS 

Per  cents  are  generally  written  as  they  are  stated;  3%%, 
4.7%,  •%%. 

Some  countries  have  a  sign,  %o,  which  means  thousandths, 
and  is  called  "per  mil."  Inasmuch  as  many  of  our  statistical 
comparisons  are  carried  out  to  thousandths,  the  employment 
of  the  per  mil  sign  would  enable  them  in  a  per  cent  to  dis- 
pense with  the  decimal  point  used  to  denote  the  tenths. 

Baseball  records  are  reported  in  thousandths,  a  batter's 


NUMBERS  AND   PROCESSES  133 

average  being  given  as  .297,  .315,  etc.  For  the  sake  of 
uniformity,  unnecessary  ciphers  are  used;  as,  .300,  .290,  etc. 
These  records  are  sometimes  stated  by  the  unthinking  as 
297  per  cent,  315  per  cent,  etc.  If  the  term  per  cent  is  used, 
it  should  be  29.7  %,  etc.  In  giving  a  record  orally,  a  player 
is  said  to  be  batting  297,  300,  etc.,  omitting  the  word  "thou- 
sandths." 

ROMAN  NUMBERS 

The  use  of  Roman  numbers  is  limited  to  the  num- 
bering of  the  different  books  of  a  work  issued  in  vol- 
umes; to  the  numbering  of  chapters,  sections,  etc., 
of  a  book;  to  inscriptions  showing  the  date  of  the 
erection  of  a  building,  etc.;  to  the  figures  on  the  dial 
of  a  watch  or  clock,  etc. 

In  some  countries  a  Roman  number  is  used  in  a 
date  to  indicate  the  month,  VII-1-18,  meaning  July  1, 
1918.  This  obviates  the  confusion  existing  in  the 
mind  of  a  person  in  this  country,  who  does  not  know 
whether  7-1-18  means  July  1,  1918,  or  January  7, 
1918,  there  being  no  universal  agreement  as  to  the 
matter.  Some  argue  that  the  month  should  precede, 
as  is  the  case  when  it  is  written  out;  others  claim  that 
the  day  first,  followed  in  the  order  by  the  month  and 
the  year,  is  the  more  logical  arrangement. 

A  person  desiring  to  denote  the  month  by  a  number 
should  use  the  Roman  form;  in  which  case  l-VII-1918, 
or  VII-1-1918  would  mean  the  seventh  month,  whether 
written  in  the  first  place  or  the  second. 

Roman  notation  employs  the  following  characters: 

I        V        X        L         C  D          M 

to  denote  respectively 

1    5    10    50    100    500    1000 


134          WALSH'S  BUSINESS  ARITHMETIC 

The  ones  to  9,  the  tens  to  90,  the  hundreds  to  900, 
etc.,  are  written  as  follows: 


1  1 

X  10 

C  100 

M  1000 

II  2 

XX  20 

CC  200 

MM  2000 

III  3 

XXX  SO 

CCC  300 

MMM  3000 

IV  4 

XL  40 

CD  400 

IV  4000 

V  5 

L  50 

D  500 

V  5000 

VI  6 

LX  60 

DC  600 

VI  6000 

VII  7 

LXX  70 

DCC  700 

VII  7000 

VIII  8 

LXXX  80 

DCCC  800 

VIII  8000 

IX  9 

XC  90 

CM  900 

IX  9000 

Note  that 

The  value  of  V  or  of  X  is  decreased  by  the  value  of 
an  I  immediately  preceding  it. 

The  value  of  L  or  of  C  is  decreased  by  the  value  of 
an  X  immediately  preceding  it. 

The  value  of  D  or  of  M  is  decreased  by  the  value  of 
a  C  immediately  preceding  it. 

No  letter  is  employed  more  than  three  times  in 
expressing  a  number,  excepting  IIII  on  a  clock  face. 

Thousands  beyond  3000  are  indicated  by  a  line  above 
IV,  V,  VI,  etc. 

To  write  the  Roman  numbers  between  11  and  19, 
inclusive;  between  21  and  29,  inclusive;  etc.;  affix 
the  characters  representing  1  to  9,  respectively,  to 
the  characters  denoting  10,  20,  30,  etc.,  respectively. 

ORAL  EXERCISES 

1.  Express  in  Roman  numbers: 

a  23        b  34        c  45        d  56        e  67        /  78 

2.  State  the  values  of: 

a  XCIX        6  LXXIV        c  XLVI        d  XXXVII 


NUMBERS  AND  PROCESSES  135 

To  write  the  Roman  numbers  between  101  and 
199,  inclusive;  between  201  and  299,  inclusive,  etc., 
affix  the  character  representing  1  to  99,  respectively, 
to  characters  denoting  100,  200,  300,  respectively. 

3.  Express  in  Roman  numbers: 

a  124         b  347         c  589         d  799         e  919 

4.  State  the  values  of 

a  CCXL         b  CDXIX          c  DCCX      d  CMXCIX 
e  DCXV        /  DCCVI  g  CMLV      h  DCXLVII 

To  write  the  Roman  numbers  between  1001  and 
1999,  inclusive;  between  2001  and  2999,  inclusive, 
etc.,  affix  the  characters  representing  1  to  999,  re- 
spectively, to  the  characters  representing  1000,  2000, 
3000,  etc.,  respectively. 

5.  Express  in  Roman  numbers: 

a  1234         b  2345         c  3457         d  2968 
e  4067        /  5380         g  2799         h  6042 

6.  State  the  values  of 

a  MDCLX  b  MMCDL  c  MMMXC 
d  MCMXC  e  VIIDCC  /  IXCMXL 
g  CMLIX  h  MCDLX  i  DCCCXC 

"ROUND"   NUMBERS 

WRITTEN  EXERCISES 

1.  The  following  is  the  average  quantity  of  cotton 
produced  annually  in  the  United  States  during  a 
10-year  period  preceding  the  last  census,  expressed  in 
thousands  of  bales:  Texas,  2838;  Georgia,  1513; 
Mississippi,  1370;  Alabama,  1155;  North  Carolina, 
931;  Arkansas,  811;  Louisiana,  717;  South  Carolina, 


136          WALSH'S  BUSINESS  ARITHMETIC 

547;  Oklahoma,  540;  Tennessee,  310;  Florida,  62; 
Missouri,  38;  Virginia,  16.  Find  the  total  in  thou- 
sands of  bales. 

2.  How  much  smaller  is  it  than  the  1917  crop  of 
12,000,000  bales? 

3.  In  a  year  the  sugar  production  in  millions  of 
pounds   was   as   follows:     Beet    Sugar,    989%;     Cane 
Sugar,  437%;  Maple  Sugar,  12.     Find  the  total  weight 
in  millions  of  pounds. 

4.  Complete  the  following  statistics  of  cotton  pro- 
duction, and  find  the  totals;  (e),  (/),  (0r),  and  (h). 


Thousands 

Millions 

Millions 

Millions 

States 

of  bales 

of  pounds 

of  pounds 

of  pounds 

(«) 

(6) 

(e) 

(d) 

Texas 

2838 

141.9 

142 

142 

Georgia 

1513 

75.65 

75^ 

76 

Miss'ssippi 

1370 

68.5 

68K 

58 

Alabama 

1155 

57.75 

57^ 

58 

etc. 

etc. 

etc. 

etc. 

etc. 

Totals  (e)  (/)  (g)  (/*) 

•     Take  (a)  from  Example  1. 

In  (6)  assume  the  weight  of  a  bale  as  500  pounds.  Divide  (a)  by  2,  and 
point  off  1  decimal. 

In  (c),  rewrite  (6),  rejecting  decimals  to  .25,  substituting  %  for  these 
from  .  26  to  .  75,  and  increasing  the  integer  by  1  when  the  decimal  is  greater 
than  .75. 

In  (d)  use  integers  exclusively,  rejecting  decimals  in  (6)  to  .5,  and  in- 
creasing the  integer  by  1  when  the  decimal  is  .5  or  more. 

In  selling  a  quantity  of  cotton,  every  bale  must  be 
weighed,  its  net  weight  ascertained,  etc.  In  the  news- 
paper reports  of  sales,  the  number  of  bales  is  sufficient. 
In  production  statistics,  .the  number  of  thousands  of 
bales  answers  every  purpose. 


NUMBERS  AND   PROCESSES 


137 


REPRESENTING    QUANTITIES   GRAPHICALLY 

The  first  map  shows  the  cotton  belt  of  the  United 
States  with  relative  production  of  the  cotton  states. 
The  next  map  shows  the  cotton  production  of  the 
world. 


COTTON 

AVERAGE  ANNUAL 

PRODUCTION 


138 


WALSH'S  BUSINESS  ARITHMETIC 


STRAIGHT  LINE  GRAPHS 

WRITTEN  EXERCISES 

1.  From  the  table  of  the  average  production  of 
cotton  in  the  United  States,  complete  the  following 
graph : 


Average  Annual  Cotton  Production  for  Ten  Years 


States 


Millions  of  pounds 


Texas 

Georgia 
Mississippi 

= 

EEE 

— 

.= 

- 

— 

— 

— 

— 

— 

— 

- 

etc. 
Virginia 

10  20  30  40  50 


70  80  90  100  110  120  130  140 


Each  perpendicular  space  represents  10  million  of  pounds. 
The  line  for  Texas  extends  a  trifle  beyond  the  line  for  140 
millions;  that  for  Georgia,  a  trifle  more  than  one-half  the 
distance  between  70  and  80  millions,  etc. 

2.  The  accompanying  summary  shows  the  effects 
of  irrigation  on  two  fields  of  oats  and  two  of  wheat. 


Irrigation 

Production  per  Acre 

Oats 

Wheat 

None 
13  in.     10  in. 
20  "      18  " 

425  Ib. 
1424  " 
2060" 

540  Ib. 
1200" 
1950  " 

NUMBERS  AND    PROCESSES 


139 


a  Find  the  production  per  acre  in  bushels,  taking  32 
pounds  of  oats  to  the  bushel  and  60  pounds  of  wheat. 

b  Make  a  graph  based  upon  the  number  of  pounds 
of  each  to  the  acre  raised  under  the  several  conditions. 


Pounds 
of 
Grain 
per 
Acre 

Oats                          Wheat 

II 

Inches  of  Water  Applied 

0 

13 

20 

0 

10 

18 

2000 
1800 
1600 
1400 
1200 
1000 
800 
600 
400 
200 
0 

I 

II 

III 

IV 

V 

VI 

c  At  96  cents  a  bushel  for  oats  and  $2.10  a  bushel 
for  wheat,  find  the  value  of  each  crop  (I  to  VI). 

d  Make  a  graph  based  upon  the  value  of  each  crop 
an  acre. 


140 


WALSH'S  BUSINESS  ARITHMETIC 


BROKEN-LINE  GRAPHS 

The  following  graph  shows  the  per  cent  of  those 
6  to  20  years  of  age  in  a  certain  city,  who  are  attend- 
ing school. 

In  this  graph  the  horizontal  lines  indicate  the  per 
cents  and  the  vertical  lines  the  ages.  On  each  of  the 
latter  the  proper  per  cent  is  noted  by  a  point,  and  a 
line  is  drawn  from  one  point  to  the  next. 

Rat a  Taart  of  ago, 

6         7         8         9         10       11       12       13       14       15       16       17       18       19       20 


70JC- 


50*- 


30 


\ 


ORAL  EXERCISES 

1.  About  what  per  cent  of  the  children  (a)  6  years 
of   age   are   in    school?     (6)    7    years?     (c)  8    years? 
(d)  11  years?     (e)  14  years? 

2.  What  age  shows  the  largest  per  cent  of  pupils 
in  school?  , 

3.  About  what  per  cent  of  persons  19  years  of  age 
are  not  in  school? 

The  average  selling  price  of  cattle  by  months  during  10 
years  is  shown  in  the  next  graph.  The  price  for  each  month 
is  found  in  the  center  of  the  monthly  space. 


NUMBERS  AND  PROCESSES 


141 


ORAL  EXERCISES 

1.  Give  the  average  price  for  each  month. 

2.  (a)  In  what  month  did  cattle  average  the  lowest 
price?      (6)  What  was  the  price?     (c)  In  what  month 
did   they   average   the  highest?     (d)  What   was   this 
price? 

MAKING  A  BROKEN-LINE   GRAPH 

In  making  a  broken -line  graph,  use  cross-ruled 
paper,  if  it  is  at  hand,  thus  saving  time  in  laying  out 
the  necessary  vertical  lines. 


142 


WALSH'S  BUSINESS  ARITHMETIC 


WRITTEN  EXERCISE 

Make  a  graph  showing  the  average  prices  for  12 
months,  as  follows:  $5.92,  $6.08,  $6.36,  $6.47,  $6.44, 
$6.22  $5.63,  $5.88,  $5.66,  $5.84,  $5.80,  $6.02. 

READING  METERS 

Every  housekeeper  should  read  the  gas  meter  at  the 
time  it  is  read  by  the  agent  of  the  company,  and  should 
keep  a  record  of  the  readings  and  the  date  in  order 
to  be  able  to  check  up  the  bill  when  it  is  rendered. 

_.  _          The  small  dials  at 

,^•1  i^^^. 

the  top  are  ignored 
in  reading  the  meter, 
being  used  merely  to 
test. 

When  the  hand 
makes  a  complete 
revolution  of  the 
dial  marked  "100 


CUBIC 
FEET 


Dials  of  a  Gas  Meter 


thousand,"  it  indicates  the  consumption  of  100,000 
cubic  feet  of  gas.  The  passage  of  the  hand  over  each 
of  the  ten  divisions,  shows,  therefore,  the  consumption 
of  Ko  of  that  quantity,  or  10,000  cubic  feet.  Since  the 
hand  in  this  dial  has  passed  eight  divisions,  it  shows  a 
consumption  of  80,000  cubic  feet. 

The  hand  of  this  first  dial  moves  from  left  to  right, 
that  of  the  second  dial  from  right  to  left.  For  this 
reason  the  order  of  the  dial  numbers  is  reversed.  As 
each  division  of  the  second  dial  indicates  Xo  of  10,000 
cubic  feet,  this  dial  shows  a  consumption  of  4,000 
cubic  feet,  the  hand  having  passed  four  divisions. 


NUMBERS  AND  PROCESSES 


143 


It  is  in  the  reading  of  this  dial  that  mistakes  are 
made  by  the  beginner,  who  forgets  that  the  motion 
of  this  hand  is  from  right  to  left,  and  that  it  has  not 
reached  the  5th  division. 

The  hand  of  the  last  dial  moves  from  left  to  right. 
As  it  has  passed  two  divisions,  the  consumption  is 
over  200  cubic  feet.  The  excess  is  ignored,  being  left 
for  the  next  reading. 

The  consumption  recorded  above  is  84,200  cubic 
feet,  which  indicates  the  quantity  of  gas  that  passed 
through  the  meter  since  its  installation. 

ORAL  EXERCISES 

1.  Read  the  following  dials,  which  show  Mr.  Han- 
Ion's  meter  records  for  six  successive  months. 

Oct. 2, 1919  Nov.1,1919 


Dec. 2 ,1919 


Jan. 2, 1920 


Feb.  1,1 920 


Mcb.3,1920 


2.  Give  the  difference  (a)  between  the  reading  of 
December  and  that  of  January.  (6)  Between  the 
reading  of  January  and  that  of  February. 


144          WALSH'S  BUSINESS  ARITHMETIC 

A  Gas  Bill 


Jay  A.  Lindon 
4235  Fairfax  Road 
To  KINGS  COUNTY  LIGHT  COMPANY,  Dr. 
384  Midwood  Ave. 
Telephone,  Sunset  2700 

Index  of  Meter,  Sept  2,  1919.                 26,300  cu.  ft. 
"      "       "       Aug.  2,  1919.                23,500  "     " 

I           2.52 
.28 

2.24 

"      "       "       To  supply  of                   2,800  "     "  @  90j 
Discount  of  Iff  per  100  cu.  ft. 

Received  Payment.  .  .Sep.  25,.  .  .1919. 
per  .  .  .  Frank  Regan  .  .  .  ,  for  the  Company 

Mrs.  Lindon  compares  this  bill  with  the  memoran- 
dum of  her  meter  readings.     This  she  keeps  in  the 

following  form: 

GAS  CONSUMPTION 


Date 

Reading 

Cu.  ft. 
Used 

Cost  at 
90f*  per 
1000  cu.  ft. 

Discount 

Net 

Bill 
paid 

1919 

Aug.  2 

23,500 

2400 

2 

16 

24 

1 

92 

VIII-18-19 

Sep.    2 

26,300 

2800 

2 

52 

28 

2 

24 

IX-25-19 

Oct.    2 

30,000 

Nov.  1 

34,100 

Dec.  2 

38,300 

1920 

Jan.    2 

42500 

Feb.    1 

43.500 

Mar.  3 

46,700 

WRITTEN  EXERCISES 

1.  Complete  the  foregoing  memorandum,  inserting 
(a)  the  quantity  of  gas  used  each  month,  (b)  the  gross 
cost,  (c)  the  discounts,  and  (d)  the  net  amount. 


NUMBERS  AND  PROCESSES  145 

2.  Find  (a)  the  totals  for  the  eight  months,    (b)  The 
average  consumption  a  month. 

3.  The  daily  allowance  of  gas  to  a  room  of  an  army 
officer  on  post  duty  is  50  cubic  feet  from  Sep.  1  to 
Apr.  30,  inclusive,  and  30  cubic  feet  from  May  1  to 
Aug.  31,  inclusive.     Find  the  yearly  allowance  for  the 
lights  of  three  rooms  at  80  cents  a  thousand  cubic  feet. 

4.  If  an  ordinary  open-flame  burner  uses  5  cubic 
feet  an  hour,  what  is  the  cost  of  an  hour's  light  at  the 
rate  of  $1  a  1000  cubic  feet? 

5.  Mr.  Jones  formerly  used  2  open-flame  burners, 
each  consuming  5  cubic  feet  of  gas  an  hour.     He  re- 
placed both  by  a  single  mantle  burner,  using  4  cubic 
feet  of  gas  an  hour.     What  did  he  save  in  a  year  by 
the  change  if  he   used  gas  for  1000  hours,  at  $1  a 
1000   cubic   feet,  and  paid   25  cents  each   for   three 
mantles  for  the  new  burner? 

SELLING  ELECTRIC   CURRENT 

The  unit  for  measuring  electrical  work  is  the  watt-hour 
or  the  kilowatt-hour,  the  latter  being  1000  watt-hours. 

A  25 -watt  electric  lamp  will  use  25  watt-hours  of 
energy  per  hour,  or  a  kilowatt-hour  in  40  hours. 

The  amount  used  is  recorded  by  a  meter  having 
dials  similar  to  those  employed  on  a  gas  meter. 

One  form  of  electric  meter  shows  the  number  of 
"kilowatt-hours"  on  four  dials  similar  to  those  em- 
ployed on  the  gas  meter. 

MARKING  GOODS 

For  the  guidance  of  salespeople  in  large  stores, 
the  selling  price  of  each  article  is  marked  on  it,  gen- 


146          WALSH'S  BUSINESS  ARITHMETIC 

erally  in  plain  figures.  For  the  information  of  the 
manager,  etc.,  the  cost  is  also  noted. 

In  giving  the  latter,  letters  are  used  instead  of  figures, 
in  order  that  it  may  not  be  disclosed  to  the  customer. 

In  selecting  the  letters,  a  word  or  combination  of 
words  containing  at  least  ten  letters  is  employed. 
"Frank  White,"  for  instance. 

Each  letter  in  these  two  words  represents  the  figure 
written  under  it. 

FRANK     WHITE 
12345      67890 

The  number  375  is  written  AUK;   429,  NRT;   etc. 

THE  REPEATER 

In  writing  a  number  having  two  consecutive  figures 
alike,  an  eleventh  letter  is  used,  which  is  not  con- 
tained in  the  10 -letter  key. 

Thus,  $1.12  is  written  FDR,  the  second  1  being 
represented  by  the  repeater,  D;  $3.99  is  written 
ATD. 

WRITTEN  EXERCISES 

1.  Using  "Frank  White"  as  the  key,  and  "D"  as 
the  repeater,  express  by  letters: 

a  $4.41         b  $.39         c  $3.22         d  $1.76         e  $12.84 
/     5.98        g     .97         h     6.04         i     3.21         j     22.05 

2.  Using  "Quick  Reason"  as  the  key,  and  taking 
N,  the  last  letter,  as  the  repeater,  express  the  fol- 
lowing by  letters: 


NUMBERS  AND  PROCESSES  147 

a  $3.00         b  $.27         c  $8.04         d  $3.95         e  $20.08 
/     4.32         g     .55         h    9.99         i     4.68        j     12.23 

Sometimes  when  a  price  is  below  $1,  a  dealer  prefers 
to  use  three  letters,  and  to  use  four  when  it  is  below  $10. 
In  such  a  case,  he  uses  a  letter  which  is  to  be  disre- 
garded. For  instance,  he  represents  $.99  by  BSN,  or 
SNB,  with  the  key  "Quick  Reason,"  using  B  as  the 
letter  to  be  omitted. 

ORAL  EXERCISES 

Read  the  following,  for  which  the  key  is  "Quick 
Reason,"  and  in  which  B  is  superfluous. 

a  RON    b  CNK     c  BAO      d  UKO      e  BSRI       f  1C 
g  IAN     h  EAE     i  SBR       j  QIE        k  SNBO       I  KN 

If  it  is  desired  to  mark  the  cost  by  the  use  of  letters, 
as  well  as  the  selling  price,  a  different  key  is  used  for 
each. 

With  "Frank  White"  as  the  key  for  the  cost,  and 
"Quick  Reason"  as  the  key  for  the  selling  price,  with 
D  for  the  repeater  in  the  former,  and  N  in  the  latter 
and  B  for  the  superfluous  letter,  read  the  following,  the 
upper  line  representing  the  cost  and  the  lower  the 
selling  price. 

BID          ,  FHK  ADE          ,  FRTA  WIA 

QNU          *  UON          c  CEK          l  QKIO        e  ASU 

WRITTEN  EXERCISES 

1.  Using  the  last  two  keys  for  the  cost  and  the 
selling  price,  respectively,  express  each  in  letters, 


148          WALSH'S  BUSINESS  ARITHMETIC 

increasing  the  cost  by  the  given  rate  to  obtain  the 
selling  price. 

a  Cost  $1.80,  selling  price,  35  %  advance 
b  Cost    9.20,      "          "      20% 
c  Cost    8.40,      "          "      33%% 
d  Cost    2.40,      "          "      37%% 
e  Cost    4.96,      "          "      43%% 

2.   Find  the  per  cent  of  advance  on  goods  marked 
as  follows: 

VTW        ,  RAPE  FKE         ,  ACD  VTIN 

*  QUO          °  IOAO          c  QEK         l  CAR        '  QCER 


CHAPTER  TWO 

PROPERTIES    OF    NUMBERS 

COMPOSITE  NUMBERS 

A  number  that  exactly  contains  a  number  other 
than  itself  or  1,  is  called  a  composite  number. 

4,  6,  8,  9,  10,  etc.,  are  composite  numbers. 

An  exact  divisor  of  a  number  is  called  a  factor  of 
the  number. 

2  is  a  factor  of    4,  of  6,  of  8,  of  10,  etc. 

3  "  "      "      "    6,  of  9,  of  12,  etc. 
5   "  "      "      "  10,  of  15,  of  20,  etc. 

ORAL  EXERCISES 
1.   Give  the  factors  of 


a  6 

b 

10 

c 

14 

d 

15 

e 

21 

/ 

22 

g  26 

h  33 

i 

34 

3 

35 

k 

38 

I 

39 

m 

46 

n  51 

o  55 

P 

57 

Q 

58 

r 

65 

s 

69 

t 

77 

u  85 

v  87 

w 

91 

X 

95 

y 

115 

z 

119 

2.   Give  the  two  equal  factors  of 

a  4        69        c  25        d  49        e  121        /  169 

PRIME  NUMBERS 

A  number  that  is  exactly  divisible  only  by  itself 
and  1  is  called  a  prime  number. 

1,  2,  3,  5,  7,  etc.,  are  prime  numbers. 

149 


150          WALSH'S  BUSINESS  ARITHMETIC 

ORAL  EXERCISES 

1.  Give  the  prime  numbers  between 

a  10  and  30        b  30  and    50        c    50  and    70 
d  70  and  90        e  90  and  110        /  110  and  130 

2.  Give  the  prime  factors  of: 

a  30     6  42    c  78    d  66     e  70    /  102    g  110    h  114 

3.  Give  all  of  the  exact  divisors  of  each  of  the  fore- 
going numbers. 

A  number  that  is  a  factor  of  each  of  two  or  more 
numbers  is  called  a  common  factor  of  these  numbers. 

2  is  a  common  factor  of  8  and  14,  3  is  a  common 
factor  of  15  and  24,  etc. 

Two  or  more  numbers  that  have  no  common  factor 
are  said  to  be  prime  to  each  other;  4  and  9,  for  instance; 
6  and  25;  etc. 

ORAL  EXERCISES 

1.  Give  a  common  factor  of: 

a  30  and  63        6  22  and  56        c  25  and  70        d  21  and  56 

2.  Give  two  common  factors  of: 

a  30  and  42       b  42  and  66       c  42  and  70       d  66  and  105 

3.  Give  the  largest  common  factor  of: 

a  18  and  24  6  14  and  56  c  12  and  30  d  52  and  91 
e  26  and  65  /  34  and  85  g  21  and  93  h  37  and  74 
i  69  and  92  j  34  and  51  k  68  and  85  /  65  and  91 

4.  Express  each  of  the  following  fractions  in  its 
lowest  terms  by  dividing  its  numerator  and  its   de- 


NUMBERS  AND  PROCESSES  151 

nominator  by   their  largest  common  factor    (greatest 
common  divisor). 

a  %3        b  %4        c  %5        d  % 
e  %         /  %         9  %         h 


A  number  that  is  divisible  by  another  number 
is  called  a  multiple  of  the  latter.  4,  6,  8,  16,  etc., 
are  multiples  of  2.  6,  24,  42,  96,  etc.,  are  multiples 
of  6. 

A  number  that  is  a  multiple  of  two  or  more  numbers 
is  called  a  common  multiple  of  these  numbers.  6,  18, 
24,  etc.,  are  common  multiples  of  2  and  3.  24,  36,  72, 
etc.,  are  common  multiples  of  4  and  6. 

The  smallest  number  that  is  a  multiple  of  two  or 
more  numbers  is  called  their  least  common  multiple. 
(L.  C.  M.) 

The  least  common  multiple  of  two  or  more  prime 
numbers  is  the  continued  product  of  these  numbers. 

The  L.  C.  M.  of  2,  3,  and  7  is  2  X  3  X  7. 

The  least  common  multiple  of  two  or  more  numbers 
prime  to  each  other  is  also  their  continued  product. 

The-L.  C.  M.  of  4  and  9  is  4  X  9;  of  6  and  25  is 
6  X  25;  of  5,  8,  and  9  is  5  X  8  X  9;  of  8  and  9  is  8  X  9. 

In  finding  the  least  common  multiple  of  several 
numbers,  omit  the  consideration  of  any  number  that 
is  a  factor  of  any  other  one. 

To  find  the  L.  C.  M.  of  4,  6,  and  8,  omit  4  since  a 
multiple  of  8  is  necessarily  a  multiple  of  4.  In  deter- 
mining the  L.  C.  M.  of  6  and  8,  consider  the  succes- 
sive multiples  of  8  (16  and  24)  until  one  is  found 
that  is  a  multiple  of  6. 


152          WALSH'S  BUSINESS  ARITHMETIC 

ORAL  EXERCISES 

1.  Give  the  least  common  multiple  of  each  of  the 
following : 

a  4  and    6  b  4,  6,  and    8  c     6  and    9 

d  9  and  12  e  2,  3,  and    5  /    4  and  14 

g  5  and  24  h  6,  8,  and  10  i  12  and  16 

j  4  and    9  k  5,  8,  and    9  I     6  and  15 

2.  Give  the  least  common  multiple  of  the  denomi- 
nators of  the  following  fractions   (least  common  de- 
nominator) : 

a  %  and  %  b  %,  %,  and  %  c%  and  %0 
d  %  and  V8  e  %,  %,  and  %  /  %  and  % 
g  %  and  %  fc  &  X,  and  %  i  Xo  and  & 

DIVISIBILITY  OF  NUMBERS 

2  is  a  factor  of  any  number  whose  last  figure  is  a 
cipher  or  is  divisible  by  2. 

5  is  a  factor  of  any  number  whose  last  figure  is  a 
cipher  or  a  5. 

3  is  a  factor  of  any  number  the  sum  of  whose  digits, 
is  divisible  by  3. 

11  is  a  factor  of  any  number  having  the  sum  of  its 
odd  digits  equal  to  the  sum  of  its  even  digits. 

The  powers  of  the  foregoing  prime  numbers  are 
factors  as  follows: 

4  (2  X  2)  is  a  factor  of  any  number  whose  last  two 
figures  are  ciphers,  or  indicate  a  number  divisible  by  4. 

8  (2  X  2  X  2)  is  a  factor  of  any  number  whose  last 
three  figures  are  ciphers,  or  indicate  a  number  divisible 
by  8. 


NUMBERS  AND  PROCESSES  153 

25  (5  X  5)  is  a  factor  of  any  number  whose  last  two 
figures  are  ciphers,  or  indicate  a  number  divisible  by  25. 

125  (5X5X5)  is  a  factor  of  any  number  whose 
last  three  figures  are  ciphers  or  indicate  a  number 
divisible  by  125. 

9  (3X3)  is  a  factor  of  any  number  the  sum  of 
whose  digits  is  divisible  by  9. 

ORAL  EXERCISES 

1.  Of  the  numbers  having  terminal  figures  as  fol- 
lows, state  which  are  divisible  by  2,  5,  4,  25,  8,  125: 

a  ...164         b  ...265         c  .  ..000         d  ...248 
e.,.200        /...475         #...625         h  . . .260 

2.  State  which  of  the  following  are  divisible  by  3; 
by  9: 

a  2345  b  5432  c  4533  d  3546 
e  4653  /  6345  g  3543  h  5334 
i  5423  j  3534  k  4365  I  3456 

A  number  that  is  divisible  by  2  and  by  3  is  divisible  by  6. 

3.  (a)  Which  of  the  numbers  in  the  last  example  are 
divisible  by  2?     (b)  Which  are  divisible  by  6? 

A  number  that  is  divisible  by  4  and  by  9  is  divisible  by  36. 

4.  Which  of  the  foregoing  are  divisible   (a)  by  4? 
(b)  By  36? 

A  number  that  is  divisible  by  two  or  more  numbers  prime 
to  each  other  is  divisible  by  their  product. 

Thus  72,  108,  144,  etc.,  being  divisible  by  4  and  by  9, 
are  divisible  by  36.  Although  48  and  132  are  divisible  by 
3  and  by  12,  they  are  not  divisible  by  3  times  12. 


CHAPTER  THREE 

REDUCTIONS 

DRILLS 

Every  arithmetic  period  should  begin  with  a  three- 
minute  drill  of  one  kind  or  other.  Besides  serving  to 
"warm-up"  the  pupils  for  the  work  to  follow,  it  is 
useful  as  a  review  of  preceding  topics,  and  as  tending 
to  develop  greater  facility  in  making  arithmetical 
combinations. 

SIGHT  EXERCISES 

In  sight  exercises  the  examples  should  be  in  the  view 
of  the  pupils  —  in  their  textbooks,  on  the  blackboards, 
etc.  Those  which  are  given  here  may  be  used  in 
several  ways.  One  day  oral  answers  may  be  required, 
the  class  standing,  each  taking  his  seat  when  he  an- 
nounces his  result.  When  there  is  time  after  the  com- 
pletion of  one  round  of  the  class,  the  pupils  again  stand, 
and  the  drill  is  continued  until  time  is  announced  by 
the  pupil  designated  to  act  as  scorer. 

When  a  pupil  gives  an  incorrect  result,  the  teacher 
says  nothing;  but  no  answers  to  subsequent  questions 
are  considered  until  some  pupil  corrects  the  error 
previously  made.  The  next  pupil  answers  the  question 
following  the  one  just  answered  correctly,  etc. 

The  scorer  notes  on  the  blackboard  the  number  of 
questions  answered  and  the  number  of  errors  made. 

154 


NUMBERS  AND  PROCESSES  155 

When  the  same  set  of  examples  is  taken  up  again,  the 
result  should  show  an  improvement. 

WRITTEN  ANSWERS 

Another  way  to  use  some  of  these  exercises  is  to  have 
all  of  the  pupils  write  on  slips  their  answers  to  the  desig- 
nated questions.  The  answers  are  then  announced, 
and  each  pupil  checks  his  correct  ones  and  notes  their 
number.  The  scorer  should  ascertain  and  record  the 
class  average. 

REDUCING  FRACTIONS 

CHANGING  AN  IMPROPER  FRACTION  TO  A  MIXED 
NUMBER 

SIGHT  EXERCISES 
1.   How  many  dollars  are  there  in  85  quarter  dollars  ? 


PROCESS 

$85 
—  =  $21%.     Ans. 

Change  the  improper  fraction  8%  to  a  mixed  number 
by  dividing  85  by  4. 


2.   Express  as  a  mixed  number: 

a  "A         b  %        c    %        d  %  e  «% 

f  %        g  <%        h   %        i  *°/7  j  9% 

fc  %        I  %        ro  %        n  7%  o  % 

P  %         q  %         r    %         s   %  t   % 

u  %         v  %         w  %         x  %  y  % 


156          WALSH'S  BUSINESS  ARITHMETIC 

CHANGING  A  MIXED   NUMBER  TO  AN  IMPROPER 
FRACTION 

3.   How  many  quarters  are  there  in  $24%? 


PROCESS 

$24%  =  $%  Ans. 

Think  96  (4  times  24),  99  (adding  3).  Make  99 
the  numerator  of  the  improper  fraction,  and  4  its 
denominator. 


4.   Change  to  an  improper  fraction: 

b  14Ko  e  15%  d 

/  30%  g  40%  h 

j   19%  k  17%  I  5%> 

m  25%         n  31%  o  20%  p 

q    22K          r  24%  *  26%  t 
u    11%         v   18% 


EXPRESSING  A  FRACTION  IN   LOWEST  TERMS 
5.   What  fraction  of  a  yard  is  (a)  27  inches?     (6)  24 
inches?     (c)  32  inches? 


PROCESS 

(a)  27  in.  =  %  yd.  =  %  yd.  Ans. 
(6)  24  in.  =  %  yd.  =  %  yd.  Ans. 
(c)  32  in.  =  %  yd.  =  %  yd.  Ans. 

(a)  Reduce  %  by  dividing  both  terms  by  9. 

(b)  Reduce  %  by  dividing  both  terms  by  12. 

(c)  Reduce  %  by  dividing  both  terms  by  4. 


A  pupil  who  does  not  see  at  once  that  9  is  the  greatest  common  divisor 
of  27  and  36  may  first  reduce  %  to  &  by  dividing  each  term  by  the  com- 
mon factor,  3. 

Before  announcing  %  as  the  answer,  he  should  be  expected  to  note  that 
it  is  further  reducible  to  %,  9  and  12  having  3  as  a  common  factor. 


NUMBERS  AND  PROCESSES  157 

6.   Express  in  lowest  terms : 


a  %  b  %  c    %  d  % 

/  %  9%  h    %  i  %  j  % 

k  %  /  %  m  %  n  %  o  % 

p  %  g  %  r    %  ^  %  t   %o 

t*  %  ^  %  w  3%4  a;  %  y  % 

7.  Give  the  greatest  common  factor  of: 

a  18  and  27  6  25  and  60  c  16  and  36 

d  36  and  48  e  40  and  72  /  20  and  75 

g  48  and  72  h  36  and  54  i  15  and  50 

j  75  and  90  fc  36  and  60  I  20  and  75 

8.  What  is  the  greatest  common  factor  of  57  and  95  ? 


PROCESS 

A  pupil  that  does  not  see  at  once  that  19  is  a 
common  factor  of  57  and  95,  should  note  that  both 
57  and  95  are  composite  numbers.  Obtaining  3 
and  19  as  the  factors  of  57,  he  tests  19  as  the  divisor 
of  95. 


9.   Express  in  lowest  terms: 

a  %         b  %         c  %         d  %         e  % 
/  %        g  %        h  %        i  %        j  % 


SIMPLIFYING  A  COMPLEX  FRACTION 

10.   What  fraction  of  a  rod  (16#  feet)  is  (a)  12#  ft.? 

9%  ft.? 


158          WALSH'S  BUSINESS  ARITHMETIC 

PROCESS 

Express  each  as  a  complex  fraction  of  a  rod  by 
writing  16%  as  the  denominator.  Simplify  the  com- 
plex fractions. 

12%  25 

W  E«  *•  •  M  rf 


(a)  Multiply  both  terms  of  the  complex  fraction 
by  2.  (6)  Multiply  both  terms  by  6,  the  least  com- 
mon denominator  of  %  and  %. 

11.   Express  as  a  simple  fraction: 

1%         ,   2%  3%         ,  4K  5% 

ct  —        o  —  c  —        a  —         6  — 

4  3  7  8,9 

—        A       &  A       •_!       •  8 

^l/  "     r"t\/  Q3/  G2/  1  HI/ 

,2%         .  8M  1%  5%  4% 

fc_±f  /-^  771-^  n—  0    — 

Ql/  1 2/  1 1/  017  Ql/ 

0/2  1/5  1/4  ^73  »  "72 

7}    O   7"    S    *  

Y  VA        *  2/io  2^  3^  4% 

^3^        ^2K          ^tt        ^.3^         7W 


EXPRESSING  A  COMMON  FRACTION  AS  A  DECIMAL 
12.   \Vhat  decimal  of  a  pound  is  an  ounce? 

PROCESS 

1  oz.  =  KG  lb.  =  .0625  Ib. 

Think  of  &  as  %  of  &  which  is  %  of  .25.     This  is 
or  .0625. 


NUMBERS  AND  PROCESSES  159 

13.  Express  as  a  decimal: 

a  1A  b^  c  %  d%  e  % 
f  %  9%  h  fa  i  %  j  % 
k  YB  I  %  m  Ko  n  fa  o  %> 

P    r&  Q  /oO  f       720  ^     /80  '     725 

u  fa         v  fa  .       w  %o         x  %o         y  fa 
CHANGING  A  DECIMAL   TO   A  COMMON  FRACTION 

14.  Change  to  a  common  fraction,  lowest  terms: 
(a)  .87.     (6)   .124.     (c)  .0275. 


PROCESS 

(a)  .87  =  %0,  Ans. 

(6)   .124  =  "ft™  =  %o,  Ans. 

(c)  -.0275  =  27Koooo  =  5^ooo  =  %o,  Ans. 

(a)  The  common  fraction  %o  is  expressed  in  lowest 
terms  since  87  is  divisible  by  neither  2  nor  5. 

(6)  Express  as  a  common  fraction  and  reduce  to 
lowest  terms  by  dividing  both  terms  by  4. 

(c)  If  you  do  not  observe  that  both  terms  are  divis- 
ible by  25,  divide  twice  by  5. 


15.   Express  as  a  common  fraction  —  lowest  terms : 


a  .5 

b   .25 

c    .33 

(2  .125 

c  .008 

/   -8 
k  .6 

g  .45 
I    .06 

/*    .05 

m  .08 

i    .025 
n  .375 

j  .012 
o  .037 

P  -7 
u  A 

q  .32 
v   .09 

r    .44 
w  .56 

5    .625 

x  .875 

*  .045 
y  .168 

DENOMINATE  NUMBERS  —  LOWER  TERMS 
16.   A  vessel  made  a  trip  from  Liverpool  to  New 
York  in  5  days   12  hours.      How  many  hours  were 
consumed  in  making  the  trip  ? 


160          WALSH'S  BUSINESS  ARITHMETIC 


PROCESS 

5  da.  12  hr.  =   132  hr.,  Ans. 
Think  120  hr.  (5  times  24  hr.)  132  hr.  (adding  12  hr.) 


17.  Change  to  hours: 

a  2  da.  13  hr.          b  3  da.  20  hr.  c  4  da.  16  hr. 

d  5  da.  18  hr.          e  6  da.  11  hr.  /  7  da.  10  hr. 

g  8  da.  12  hr.          h  9  da.  15  hr.  i  8  da.  16  hr. 

18.  Change  to  ounces: 

a  4  Ib.  15  oz.           6  5  Ib.  14  oz.  c  10  Ib.  8  oz. 

d  6  Ib.  13  oz.           e  7  Ib.  12  oz.  /  20  Ib.  5  oz. 

g  8  Ib.  11  oz.           h  9  Ib.  10  oz.  i  30  Ib.  7  oz. 

19.  Change  to  quarts: 

a  13  gal.  1  qt.         b  15  gal.  2  qt.  c  17  gal.  3  qt. 

d  19  gal.  3  qt.         e  21  gal.  2  qt.  /  23  gal.  1  qt. 

g  25  gal.  1  qt.         h  31  gal.  2  qt.  i  42  gal.  3  qt. 

20.  Change  to  months: 

a  7  yr.  10  mo.        611  yr.  8  mo.  c  20  yr.  9  mo. 

d  8  yr.  11  mo.        e  12  yr.  7  mo.  /  25  yr.  7  mo. 

g  9  yr.  10  mo.        h  13  yr.  6  mo.  i  30  yr.  3  mo. 

21.  Change  to  pecks: 

a  12  bu.  3  pk.         b  32  bu.  1  pk.  c  24  bu.  3  pk. 

d  22  bu.  1  pk.        e  41  bu.  2  pk.  /  52  bu.  2  pk. 

g  15  bu.  2  pk.         h  18  bu.  3  pk.  i  61  bu.  1  pk. 

22.  Change  to  quarts: 

a  13  pk.  7  qt.          b  21  pk.  4  qt.  c  41  pk.  1  qt. 

d  14  pk.  6  qt.         e  22  pk.  3  qt.  /  51  pk.  2  qt. 

g  15  pk.  5  qt.         h  31  pk.  2  qt.  i  61  pk.  3  qt. 


NUMBERS  AND  PROCESSES  161 

23.  Change  to  inches: 

a  11  ft.  6  in.  b  21  ft.  3  in.  c  13  ft.  5  in. 

d  25  ft.  9  in.  e  15  ft.  8  in.  /  22  ft.  7  in. 

g  31  ft.  2  in.  h  33  ft.  1  in.  i  12  ft.  4  in. 

24.  Change  to  feet: 

a  33  yd.  1  ft.  b  25  yd.  1  ft.  c  43  yd.  2  ft. 

d  22  yd.  2  ft.  e  53  yd.  2  ft.          /  23  yd.  1  ft. 

g  42  yd.  1  ft.  h  24  yd.  1  ft.  i  32  yd.  2  ft. 

25.  Change  to  yards  (1  rd.  =  5%  yd.) : 

a  4  rd.  1  yd.  b  12  rd.  4  yd.          c  14  rd.  3  yd. 

d  6  rd.  2  yd.  e  10  rd.  5  yd.         /  22  rd.  2  yd. 

g  8  rd.  3  yd.  &  20  rd.  4  yd.          i  30  rd.  1  yd. 

26.  A  strip  of  embroidery  measured  %  yd.     What 
was  its  length  in  feet  and  inches? 


PROCESS 


%    yd.  =  %    times    3    ft.  =  %    ft.  =  2K    ft.  = 
2  ft.  6  in.     Ans. 

Change  %  yd.  to  feet  by  multiplying  by  3.    Change 
%  ft.  to  inches  by  multiplying  by  12. 


27.   Change  to  compound  denominate  numbers  of 
lower  denominations: 

a    %2  yd.        6  %2  yd.  c    %  yd.         d  %  yd. 

e    %  wk.        /  }i  wk.  g    %  wk.         h  %  wk. 

i    %  yr.         j   %  yr.  fc  %  yr.          /  Ko  yr. 

?7i  %  da.         n  %  da.  o    %  da.         p  %  da. 


162         WALSH'S  BUSINESS  ARITHMETIC 


EXPRESSING  A  FRACTION  OF  A  DOLLAR  AS   CENTS 

28.   When  silk  is  sold  at  $%  a  yard,  what  is  the 
price  in  cents? 


PROCESS 
$j/  =  700^  -=-  8  =  87K  cents,  Ans. 

Do  not  perform  this  division  unnecessarily.     The 
pupil  should  know  12%  cents  as  $%,  and  multiply 

by  7. 


29.  Change  to  cents: 

a    $)£              b  $X            c    $X6  d  $ 

«      $X                   /     $%                   <7     $&  /?    $ 

*    $Y*             j   $X             A:    $Ko  /   $ 

m  $K             n  $}^             o   $Ko  p  $ 

9    $^            r   $%            s    $/5o  ^    $ 

W     ^/8                 V    $%                  ^    $^5  »    $ 

HIGHER  TERMS 

30.  What  fraction  of  a  dollar  is  6%  cents? 


PROCESS 
$6%      $20 


If  you  do  not  surely  recall  the  fraction,  express 
6%  cents  as  a  complex  fraction  of  a  dollar.  Re- 
duce this  to  a  simple  fraction  by  multiplying  both 
terms  by  3.  Express  this  fraction  in  lowest  terms. 


NUMBERS  AND  PROCESSES  163 

31.  Express  as  a  fraction  of  a  dollar: 

a  1%^  b  \%%i  c    37%t  d 

f  2%£  g  W%t  h    83}^  i 

k  m  I   18%  m  SlYd  n  951        o 

p  6%t  q  33%  r    62%  s  60^         t   22% 

u  8%  v  43%  w  68%  x  65  j£         y  28% 

32.  Interest  for  144  days  is  due  on  a  loan.     What 
part  of  a  year's  interest  is  due? 


PROCESS 

144  da.  =  14%6o  yr.  =  %  yr.  Ans.  Express  the  time 
as  the  fraction  of  a  year  of  360  days.  Reduce  this 
fraction  to  lowest  terms. 


33.  Express  as  a  fraction  of  a  year: 

a  80  da.         b  108  da.         c  120  da.  d  180  da. 

e  72  da.        /  144  da.          g  135  da.  h  216  da. 

i  60  da.         j   225  da.         k  285  da.  I   215  da. 

m  45  da.         n  200  da.         o  160  da.  p  252  da. 

g  40  da.         r  320  da.         s  324  da.  <   280  da. 

34.  What  fraction  of  a  year  is  10  months  15  days? 


PROCESS 

10  mo.,  15  da.  =  10%  mos.  =  — -  yr.  =  %  yr. 

%  yr.;  or  change  10  mo.,  15  da.  to  315  da.,  or  31%60  3 
Reduce  this  fraction  to  %,  then  to  %. 


164          WALSH'S  BUSINESS  ARITHMETIC 
35.   Express  as  a  fraction  of  a  year: 


a  1  mo.  10  da. 
d  4  mo.  20  da. 
g  1  mo.  15  da. 
j  4  mo.  24  da. 
ra  9  mo.  18  da. 

b  9  mo.  10  da. 
e  2  mo.  12  da. 
h  3  mo.  18  da. 
k  7  mo.  15  da. 
n  1  mo.  20  da. 

c  6  mo.  20  da. 
/  4  mo.  15  da. 
i  3  mo.  20  da. 
1  9  mo.  45  da. 
o  4  mo.  12  da. 

36.   A   plot   of  ground   contains   600   square   rods. 
How  many  acres  and  square  rods  does  it  contain? 


PROCESS 

600  sq.  rd.  =  3  A.  120  sq.  rd.  Ans. 
Divide  600  sq.  rd.  by  160  sq.  rd.,  which  gives  a 
quotient  of  3  and  a  remainder  of  120  sq.  rd. 


37.  Change  to  acres  and  square  rods: 

a  197  sq.  rd.              b  325  sq.  rd.  c  1681  sq.  rd. 

d  968  sq.  rd.             e  487  sq.  rd.  /  3207  sq.  rd. 

g  360  sq.  rd.             h  645  sq.  rd.  i  4809  sq.  rd. 

38.  Change  to  pounds  and  ounces: 

a  57  oz.           b  73  oz.           c  100  oz.  d  164  oz. 

e  68  oz.          /  84  oz.           g  120  oz.  h  329  oz. 

i  97  oz.          j  45  oz.           &  110  oz.  I  485  oz. 

39.  Change  to  feet  and  inches: 

a  99  in.            b  35  in.            c  79  in.  d  110  in. 

e  88  in.           /  57  in.            g  93  in.  h  137  in. 

i  46  in.           j  90  in.           k  63  in.  J   150  in. 

40.  Change  to  days  and  hours: 

a  35  hr.           6  42  hr.            c  53  hr.  d  100  hr. 

e  60  hr.          /  75  hr.           g  80  hr.  h  121  hr. 

i  95  hr.          j  90  hr.            k  97  hr.  I   250  hr. 


NUMBERS  AND  PROCESSES  165 

41.  Change  to  years  and  months : 

a  98  mo.         b  87  mo.         c  45  mo.  d  109  mo. 

e  38  mo.         /  56  mo.         g  90  mo.  h  123  mo. 

i   77  mo.         j  92  mo.          k  66  mo.  I    100  mo. 

42.  Change  to  months  and  days: 

a  72  da.          b  87  da.          c   196  da.  d  164  da. 

e  45  da.         /  96  da.          g  215  da.  A  265  da. 

i  58  da.          j  69  da.          A;  257  da.  /   338  da. 

43.  Change  to  pecks  and  quarts: 

a  100  qt.          b  121  qt.        c   169  qt.  d  180  qt. 

e  201  qt.          /  150  qt.        g  243  qt.  h  325  qt. 

z   165  qt.          j  281  qt.        k  401  qt.  /    487  qt. 

44.  Change  to  bushels  and  pecks: 

a  245  pk.          b  50  pk.          c  63  pk.  d  89  pk. 

e   127  pk.          /  97  pk.          g  75  pk.  h  91  pk. 

i   169  pk.          j  85  pk.          k  59  pk.  I   77  pk. 

46.   Change  to  gallons  and  quarts: 

a  317  qt.        b  89  qt.              c  98  qt.  d  51  qt. 

e  285  qt.       /  57  qt.             g  77  qt.  h  66  qt. 

i   174  qt.        j  94  qt.              fc  83  qt.  /    71  qt. 

46.   Change  to  yards  and  feet: 

a  50  yd.          b  97  yd.          c   29  yd.  d    154  yd. 

e  88yd.         /  70yd.         g  46yd.  /*    218yd. 

i  82  yd.          j   52  yd.          k  80  yd.  /     163  yd. 

w  40  yd.          n  49  yd.          o  95  yd.  p   241  yd. 

OMITTING   "SIDE"   CALCULATIONS 

To  show  the  pupil  that  he  can  dispense  with  many 

figures  he  has  been  accustomed  to  use,  a  feature  should 


166          WALSH'S  BUSINESS  ARITHMETIC 

be  made  of  exercises  in  which  the  pupil  writes  only 
the  answers  to  examples  from  the  blackboard  or  the 
textbook.  These  exercises  should  be  more  difficult 
than  the  regular  "sight"  exercises. 

REDUCING  FRACTIONS 
Only  answers  to  be  written 

Write  answers  directly  from  the  book: 
1.   How  many  twenty-fourths  are  there  in 


PROCESS 

223%  =  53%    Ans. 

Multiply  223  by  24  and  "add  in"  17. 
Say  72  (24  times  3),  89  (adding  17);  write  9. 
Say  48  (24  times  2),  56  (carrying  8);  write  6. 
Say  48  (24  times  2),  53  (carrying  5);  write  53, 


2.  Change  to  an  improper  fraction: 

a    27%  b  32%  c  36%  d 

e  45%  /  21&  g  33%  h 

i    36%  j    11%  k  1%  / 

m  54%  n  22%,  o  39%o  p 

3.  How  many  ISth's  are  there  in  9%? 


PROCESS 


9%  =  '%    Ans. 

Multiply  18  by  9,  and  "add  in"  13. 
Think  72  (9  times  8),  85  (adding  13);   write  5, 
Think  9  (9  times  1),  17  (carrying  8);  write  17. 


NUMBERS  AND  PROCESSES  167 

4.  Change  to  an  improper  fraction: 

a   S7/®  b  9%  c  1%,  d  8fc 

e    %  /  8%  g  9%  h  6% 

i    9%  j   8%  k  4%9  I   3% 

m  7%3  n  8%  o  9&  p  6% 

5.  How  many  84ths  are  there  in  7%? 

PROCESS 

7%  =  65%4  Ans. 

Instead  of  adding  65  to  7  times  4,  add  only  5, 
adding  6  (tens),  the  next  partial  product,  to  8. 

Think  28  (7  times  4),  33  (adding  5);  write  3. 

Think  56  (7  times  8),  59  (carrying  3),  65  (adding 
6);  write  65. 

6.  Change  to  an  improper  fraction: 

a  3%  6  4%  c  7%  d  5% 

e  6%  /  8%  g  9%  *  8% 

i  4%  j  5%  fc  6%  /  7% 

m  5%  n  6%  o  7%  p  8% 

7.  Change  65%4  to  a  mixed  number. 

PROCESS 

<K%4  =  7?/84.  First  write  7  for  the  integral  part  of 
the  result,  then  write  84  as  the  denominator  of  the 
fractional  part.  Obtain  the  numerator  of  the  lat- 
ter, thus: 

Think  28  (7  times  4)  and  5  (writing  5)  are  33. 
Think  56  (7  times  8),  59  (carrying  3) 
and  6  (writing  6)  are  65.    Ans.  7% 


168          WALSH'S  BUSINESS  ARITHMETIC 

This  method  is  the  only  one  known  to  millions  of  European  pupils, 
who  are  never  taught  to  write  partial  products  in  long  division.  They 
subtract  7  times  84  from  653  by  finding  what  number  added  to  28  will  make 
the  next  higher  number  ending  in  3,  which  is  5,  etc.,  reversing  the  process 
used  in  Ex.  5,  to  change  7%  to  an  improper  fraction. 


8.   Change  to  mixed  numbers: 

a   *%  b  2%  c  '%  d  1424 

e    l%  f  *%  g  *%  h  «% 

i    *%  j  5%  k  <%  I  2% 

m  2%  n  *%  o  *%>  p 


DENOMINATE  NUMBERS 

9.   How  many  ounces  are  there  in  a  package  weighing 
23  pounds  11  ounces? 


PROCESS 

Change  23  Ib.  to  oz.  by  multiplying  16  oz.  by  23, 

and  "adding  in"  11  oz.     Use  16  as  the  multiplier. 

Think  48  (16  times  3),  59  (adding  in  ll);  write  9. 

Think  32  (16  times  2),  37  (carrying  5);  write  37. 

Ans.  379  oz. 


10.   Change  to  numbers  of  the  lower  denomination : 


a  27  bu.  5  pk. 
d  48  yr.  5  mo. 
g  29  gal.  2  qt. 
j  16  wk.  6  da. 
m  38  ft.  7  in. 

b  32  Ib.  13  oz. 
e  38  ft.  11  in. 
h  11  mo.  27  da. 
k  15  yr.  11  mo. 
n  22  Ib.  11  oz. 

c  21  da.  5  hr. 
/  43  yd.  2  ft. 
i  25  pk.  6  qt. 
I  16  rd.  2  yd. 
o  36  yr.  7  mo. 

11.  A   certain   journey   requires    179   hours.     How 
many  days  and  hours  does  it  require? 


NUMBERS  AND  PROCESSES  169 


PROCESS 

179  hr.  =  7  da.  11  hr.     Ans. 

The  integral  part  of  the  quotient  of  179  hr.  divided 
by  24  hr.  is  7;  write  7  (da.j.  To  obtain  the  number 
of  hours  remaining,  deduct  7  times  24  from  179. 

Think  28  (7  times  4),  and  1  (writing  1)  are  29. 

Think  14  (7  times  2),  16  (carrying  1),  and  1  (writ- 
ing 1)  are  11. 


12.   Change  to  compound  numbers  —  two  denomi- 
nations : 

a    191  hr.  6   157  oz.  c  257  in. 

d    223  pk.  e  354  da.  /  235  mo. 

g    389  in.  h  197ft.  i  200  hr. 

j     180  oz.  k  225  pk.  I   205  oz. 

m  475  da.  n  195  mo.  o  157  hr. 

p   365  da.  q  365  s.  r  364  far. 

WRITTEN  EXERCISES 
REDUCING  FRACTIONS 

1.   When  steel  bars  are  worth  $43.20  pen  ton,  how 
much  can  be  bought  for  $16.20? 


PROCESS 

$16.20  -^  43.20  =  16%32  =  %6  =  &  =  X  (T.)     Ans. 
Change  the  original  fraction  to  *%2  by  rejecting 
the  dollar  signs,  the  decimal  points,  and  the  ter- 
minal ciphers  of  both  terms. 

Divide  both  terms  of  l%2  by  2,  since  they  are  even 
numbers.  Divide  both  terms  of  %6  by  9,  since  the 
sum  of  the  digits  in  each  is  9.  Divide  both  terms 
of  %4  by  3.  To  complete  the  answer,  write  T.  in  a 
parenthesis. 


170          WALSH'S  BUSINESS  ARITHMETIC 

2.   Reduce  to  lowest  terms: 

a    19%88  b  «%,  c  2%6  d 


A;  1(%4  Z    1(%o 

m  *%o  n  2%0  o  18%6  p  x%2 

s  20  <    "os 


3.  A  woman  paid  $3.22  for  a  piece  of  velvet,  at  the 
rate  of  $5.22  per  yard.  What  fraction  of  a  yard  did 
she  buy? 


After  322/552  is  reduced  to  161/276,  a  common  divisor  of  161  and  276 
is  not  readily  determinable  by  inspection,  161  not  being  divisible  by  2  or 
by  3,  which  are  factors  of  276.  Employ  the  following  method: 


PROCESS 

32%52  =  1(%6  =  7/2  (yd.),  Ans. 

161 
Divide,  276  by  161.    Omit  the  quo-    46 


276 
115 
23 


tient,   1;   write   only  the  remainder,       0 
115. 

Divide  161  by  115,  writing  only  the  remainder,  46. 

Divide    115   by   46;    omitting   the   quotient,    2. 

Obtain  the  remainder,  23,  by  thinking  12  (twice 
6),  and  3  (writing  3),  are  15;  8  (twice  4),  9  (carry- 
ing 1)  and  2  (writing  2)  are  11. 

Divide  46  by  23.  Since  there  is  no  remainder,  23 
is  a  factor  of  46;  it  is,  therefore,  a  common  factor 
of  161  and  276. 

Divide  both  terms  of  the  fraction  by  23,  the  G.  C.  D. 


NUMBERS  AND  PROCESSES  171 

4.  Express  in  lowest  terms: 

Reduce  as  far  as  possible  by  dividing  both  terms  by  2,  3,  5,  etc.,  before 
using  the  foregoing  method  of  obtaining  the  greatest  common  divisor. 

a  3%2  6  2%4  c  3%0  d  3%2 

e  4%5  /  m/m  9  5%6  h  *%5 

i  4%4  j  *%4  k  3%4  I  3%o 

m  4%2  n  «%2  o  ™/m  p  *%7 

5.  A  farmer  has  231  acres  of  land  under  cultivation. 
There  are  112  acres  of  corn,  78  of  wheat,  22  of  rye,  and 
19  of  oats.     Find  for  each  of  the  foregoing  (a)  the 
fraction  it  constitutes  of  the  total,  and  (b)  the  decimal 
(4  places). 


PROCESS 

(a)  (&) 

Corn      112  acres,  *%i  =  %  =    -4848  + 
Wheat     78     "        %i  =  %  =    .3377  - 
Rye         22     "        %i  =  &    =    .0952  + 
Oats        19     "        %1  =  %i=    .0823- 
Total     231     "       2%3i       1       1.0000 
Express  each  item  as  a  fraction,  making  its  number 
of  acres  the  numerator,  and  231  its  denominator. 
For  (a),  reduce  each  fraction  to  its  lowest  terms. 
For  (6),  change  each  fraction  to  a  decimal  by 
dividing  its  numerator  by  its  denominator. 


4848  4-     Place  a  decimal  point  after  16  and 
annex  a  cipher.    Place  a  decimal 


point  in  the  quotient  immediately 

over   the   one   in    the    dividend. 

When    the    second    remainder    is 

found  to  be  16,  the  same  as  the  original  dividend, 


172          WALSH'S  BUSINESS  ARITHMETIC 


discontinue  the  division,  as  the  quotient  will  be 
48484848  ad  infinitum. 

Write  a  plus  sign  after  the  fourth  decimal  to  show 
that  the  next  figure  is  less  than  5. 

33766 
In  this  division  the  fifth  figure  is          — - 

greater  than  5.    Write  the  answer,         ' 
therefore,  as  .3377  — ,  the  minus  sign 
indicating  that  the  result  is  greater 

than  .33765. 

48 

Place  two  ciphers  after  the  decimal 

.09523      point  in  this  dividend.    Follow  the 

21)2.00  decimal  point  in  the  quotient  with 

110  a  cipher  preceding  9,  the  first  sig- 

50         nificant  figure.    Write  a  plus  sign 

8         after  2  to  show  that  the  next  figure 

is  less  than  5. 

Since    the   fifth  .08225 

figure    is    more  231)19.00 

than     5,     write  520 

the    answer    as  580 

.0823-  118 


6.   Express  as  4  place  decimals: 

a   fa  6  %  cfa  d  %! 

e  %  /  %  g  %  h  %7 

Since  the  denominator  of  a  decimal  is  a  power  of  10, 
the  prime  factors  of  which  are  2  and  5,  a  fraction 
expressed  in  lowest  terms  is  not  reducible  to  a  pure 


NUMBERS  AND   PROCESSES  173 

decimal,  unless  its  denominator  is  a  power  of  2  (2,  4, 
8,  16,  etc.);  a  power  of  5  (5,  25,  125,  625,  etc.);  or  a 
product  of  a  power  of  2  and  a  power  of  5  (10,  20,  40, 
etc.);  when  the  fraction  is  expressed  in  lowest  terms. 

7.   There  are  128  cubic  feet  in  a  cord  of  wood.     What 
decimal  of  a  cord  is  5  cubic  feet? 


PROCESS 
.625      .078125 


=  .0390625  (cord)     Ans. 


128        16  2 

Divide  both  terms  of  the  fraction  %28  by  8,  remem- 
bering that  5^8=  .625.  Divide  both  terms  of 
the  new  fraction  .62%>  by  8.  The  new  numerator 
becomes  .078%.  At  this  point  substitute  125  for  % 
without  completing  the  division. 


8.   Change  to  decimals  (carrying  out  as  many  places 
as  may  be  necessary  to  give  the  exact  value): 

a  KG  b  &          c  %         d  « 


g  %2          hyM         i 


9.   Change  to  decimals:    (a)  %5     (b)  % 


PROCESS 

(a)  %5  =  2%oo  =  .296,  Ans. 

(b)  %25  =  4%ooo  =  13%oooo  =  .01328,  Ans. 

In  (a)  change  the  denominator  to  1000  by  multi- 
plying it  by  8.  Multiply  the  numerator  by  8. 
Write  the  resulting  fraction  in  decimal  form. 

In  (6)  multiply  both  terms  of  the  fraction  by  8, 
and  of  the  resulting  fraction  by  4. 


174         WALSH'S  BUSINESS  ARITHMETIC 
10.   Change  to  decimals: 

a    %B  b    37/625  C     *%25 


11.   What  decimal  of  a  ton  of  2000  pounds  is  163 
pounds? 


PROCESS 
=  .0815  (T.)  Ans. 

Divide  the  denominator  by  1000  by  canceling 
the  three  ciphers;  divide  the  numerator  by  1000 
by  pointing  off  three  decimal  places.  Then  divide 
.163  by  2.  Be  careful  to  point  off  the  quotient 
properly.  Write  the  decimal  point.  Think  2  into 
1  does  not  go;  write  a  cipher.  Think  2  into  16 
goes  8  times;  write  8,  etc. 


12.   Change  to  decimals: 

a  %o  b  %  c  %o  d 

e  '%<>  /  %  g  117/«x>  h  %o 

i  7/&>o  j  fc  k  **%»  I  %> 


13.   The  distance  between  two  houses  is  281  rods. 
What  fraction  of  a  mile  (320  rods)  are  they  apart? 


NUMBERS  AND   PROCESSES  175 


PROCESS 


Cancel  the  cipher  in  the  denominator,  thus  divid- 
ing it  by  10.  Divide  the  numerator  by  10  by  point- 
ing off  one  decimal  place.  Reduce  further  by 
dividing  both  terms  by  4;  then  by  8. 

CHECK 

Multiply  .878%  by  320,  by  first  multiplying  it 
by  8,  then  by  4,  then  by  10. 


14.  Change  to  decimals: 

a  %o              b  *%o  c  %0  d  1(%o 

e  %o              /  *%>  <7  14Keo    .  A  2%o 

15,  Change  to  four-place  decimals.  First  multiply 
both  terms  by  2: 

a  %               &  %  c  %  d  %5 

P       IV.                                          f      9/r  fl      29/C  /»      31/r 

^      745                        J    755  W      736  "'     745 


REDUCING  DECIMALS 
WRITTEN  EXERCISES 

1.  Of  the  400  employees  in  a  store,  .3125  are  men, 
.3  are  women,  .29  are  boys,  and  the  remainder  are 
girls.  Find  (a)  the  corresponding  fraction  for  each, 
and  (6)  the  number  of  each  class  of  employees. 


176          WALSH'S  BUSINESS  ARITHMETIC 


PROCESS 

(a)         (6) 

Men  .3125  =  31%00o  =  &    =  125 

Women      .3  =  Xo    =  120 

Boys          .29      =  =  %o  =  116 

Girls  .0975  =    9%oo0  =  %0  =    39 

1.0000  4%0     400 

First  find  the  decimal  of  the  girl  employees. 
Express  each  as  a  common  fraction,  and  reduce 
the  latter  to  lowest  terms. 

TEST 

Test  results  (a)  by  employing  the  fractions  to 
ascertain  the  items  of  (6).  If  these  total  400,  the 
answers  to  both  questions  are  correct. 


NOTE:  A  common  fraction,  with  its  denominator  a  power  of  10,  cannot 
be  reduced  unless  its  numerator  is  an  even  number,  or  ends  in  5 . 

2.   Express  as  common  fractions  or  mixed  numbers. 
Write  answers  directly  from  the  book. 

a    .008  6   .075  c    6.0125  d  84.0075 


e  .179 

/  .004 

g  3.0044 

h  63.0648 

i  .084 

j  .175 

k  8.0C25 

/  57.0005 

m  .165 

n  .005 

o  7.0365 

p  70.0125 

q  .006 

r  .395 

s  9.3284 

t  25.3125 

u  .316 

v  .002 

w  5.3248 

x  40.0375 

3.   Change  the  following  complex  decimals  to  com- 
mon fractions,  lowest  terms: 

a  .03%  b  &X  c  .006% 


NUMBERS  AND  PROCESSES  177 


PROCESS 

a  .03^  =  3^/100  =  %0  =  Mo  Ans. 

b  .8#  =  8^/10  =  %  =  K    Ans. 

c  .006%  =  6%/1000  =  2%ooo  =  K5o     Ans. 

Write  each  as  a  complex  fraction.  Change  to  a 
simple  fraction  by  multiplying  both  terms  by  the 
denominator  of  the  fraction  in  the  numerator.  Re- 
duce the  simple  fraction  to  lowest  terms. 


4.   Express  as  common  fractions  or  mixed  numbers : 

a  1.83X  b  .85^  c  13.42%  d  .742% 

e  S.51X?          /  .08%  g  54.23X3  h  .384% 

i  5.06%  j   -54%i  £  77.06%  I    .210% 

DENOMINATE  NUMBERS 
WEIGHING  AND  MEASURING 

There  is  a  growing  tendency  in  the  business  world 
to  substitute  weighing  for  measuring.  The  farmer  dis- 
poses of  cabbages  in  large  quantities  by  the  ton;  olive 
oil  and  milk  are  sold  by  the  pound;  the  number  of 
bushels  in  a  given  quantity  of  grain  is  determined  by 
its  weight.  All  kinds  of  vegetables  are  retailed  by  the 
pound.  (For  Tables  see  pp.  459.) 

REDUCING  DENOMINATE  NUMBERS 
CHANGING  TO  LOWER  DENOMINATIONS 

WRITTEN  EXERCISES 

1.  A  vessel  took  14  weeks,  6  days,  18  hours  to  make 
a  trip  to  the  East  Indies.  How  many  hours  were 
required  to  make  the  trip? 


178          WALSH'S  BUSINESS  ARITHMETIC 

PROCESS 

Change  14  wk.  6  da.  to 

days  by  multiplying  7  da.  by     14  wk.  6  da.  18  hr. 
14,  and  "adding  in"  6  da.  104  da. 

However,  use  7  as  a  multi-  Ans.  2514  hr. 

plier,  but  do  not  write  it. 

Think  28  (7  times  4),  34  ("adding  in"  6);  write 
4  da.  under  6  da. 

Think  7  (7  times  1),  10  (carrying  3);  write  10. 

Change  104  da.  18  hr.  by  multiplying  24  hr.  by 
104,  and  "adding  in"  18  hr.  However,  use  24  as 
a  multiplier,  but  do  not  write  it. 

Think  96  (24  times  4),  104  (carrying  8);  write 
4  hr.  under  8  hr.,  dropping  a  line. 

Think  0  (24  times  0),  10  (carrying  10),  11  ("add- 
ing in"  1);  write  1. 

Think  24  (24  times  1),  25  (carrying  1);  write  25. 

CHECK 

See  the  reduction  of  2514  hr.  to  days,  weeks,  and 
hours,  p.  205. 

2.  Change  to  hours: 

a  15  wk.       b  12  wk.  6  da.          c  15  wk.  5  da.  15  hr. 
d  35  da.         e  21  da.  5  hr.  /  11  wk.  3  da.  21  hr. 

g  22  wk        h  33  wk.  9  hr.  i  13  wk.  9  da.  18  hr. 

3.  Change  to  ounces: 

a  24  Ib.  15  oz.  b  35  Ib.  14  oz.  c  20  Ib.  8  oz. 

d  34  Ib.  13  oz.  e  53  Ib.  12  oz.          /  55  Ib.  5  oz. 

g  42  Ib.  11  oz.  h  45  Ib.  10  oz.  i  43  Ib.  7  oz. 


NUMBERS  AND   PROCESSES  179 

4.   Change  to  quarts: 

a  19  bu.  3  pk.  7  qt.  b  37  bu.  1  pk.  4  qt. 

c  28  bu.  2  pk.  5  qt.  d  26  bu.  3  pk.  3  qt. 

e  35  bu.  1  pk.  6  qt.  /  18  bu.  2  pk.  2  qt. 

6.   Change  to  hours  (a)  38  wk.  (b)  29  wk.  9  hr. 

PROCESS 

Either  change  to  hours 

(a)  35  wk.  directly  by  multiplying 

245  da.  168  hr.  by  35,  or  employ 

Ans.  5880  hr.       the  factors  7  (da.)  and 

24  (hr.)  as  shown  above. 

(b)  29  wk.  0  da.  9  hr. 

Insert  0  da.  (the  miss-  onQ   , 

,          .       .     x  A\)5  ola. 

ing  denomination). 

Ans.  4881  hr. 

CHECK 

If  the  result  in  (a)  is  obtained  in  the  manner  shown 
above,  check  it  by  multiplying  168  hr.  by  35. 

Check  (b)  by  multiplying  168  hr.  by  29,  "adding 
in"  9  hr. 

6.  Change  to  inches: 

a  19  yd.  b  27  yd.  11  in.  c  33  yd.  2  ft.  9  in. 

d  38  yd.  e  37  ft.  10  in.  /  28  yd.  1  ft.  6  in. 

g  45  yd.  h  68  ft.  11  in.  i  43  yd.  2  ft.  7  in. 

7.  Change  to  feet: 

a  14  rd.  b  14  rd.  4  yd.  c  16  rd.  4  yd.  2  ft. 

d  22  rd.  e  24  rd.  5  yd.  /  42  rd.  3  yd.  1  ft. 

g  30  rd.  h  32  rd.  3  yd.  i  54  rd.  2  yd.  2  ft. 

8.  Change  to  pence: 

a  £19  b  £3  18s  c  £13  4s  6d 

d  £24  e  £7  16s  /  £25  9s  8d 

g  £37  h  £9  15s  i  £53  6s  7d 


180         WALSH'S  BUSINESS  ARITHMETIC 

9.   A  field  contains  85  acres  137  sq.  rd.;  how  many 
sq.  rd.  are  there  in  the  field? 


PROCESS 

15?  Write,  if  necessary,  160 

65  A.  137  sq.  rd.  (^he  number  of  square  rods 

10,537  sq.  rd.  Ans.  to  the  acre)  as  a  help. 
Use  it  as  the  multiplier. 

Think  0  (6  times  65),  7  (adding  in  7);  write 
7  sq.  rd. 

Think  80  (16  times  5),  83  (adding  in  3); 
write  3. 

Think  96  (16  times  6),  104  (carrying  8),  105 
(adding  in  1);  write  105. 

CHECK 

Check  by  dividing  10,537  by  160,  using  short 
division. 


10.  Change  to  square  rods: 

a  16  A.  127  sq.  rd.  b  43  A.  84  sq.  rd. 

c  23  A.  109  sq.  rd.  d  54  A.  96  sq.  rd. 

e  32  A.  132  sq.  rd.  /  62  A.  75  sq.  rd. 

11.  Change  to  days:    (a)  2  years  7  months  12  days, 
(b)  3  years  11  months  21  days. 


PROCESS 

(a)  2  yr.  =  720  da.  ,  (6)  3  yr.  =  1080  da. 

7  mo.  =  210  "  11  mo.  =  3330  " 

12  da.  =  12  "  21  da.  =   21  " 

Ans.     942  da.  Ans.    1431  da. 


NUMBERS  AND  PROCESSES  181 

In  reducing  the  following,  employ  either  method, 
using  the  other  one  as  a  check. 
12.   Change  to  days: 

a  2  yr.  7  mo.  19  da.  b  3  yr.  10  mo.  28  da. 

c  4  yr.  8  mo.  24  da.  d  5  yr.  11  mo.  17  da. 

e  6  yr.  9  mo.  13  da.          /  7  yr.  10  mo.  24  da. 


CHANGING  TO  HIGHER  DENOMINATIONS 

1.  A  certain  quantity  of  coal  was  consumed  in  a 
factory  in  2514  hours.  How  many  weeks,  days,  and 
hours  did  it  last? 


PROCESS 

24  hr.)2514  hr.  Divide     2514 

7  (da.)  104  (da.)  18  hr.  hr.    by    24    hr. 

Ans.       14  (wk.)    6  (da.)  18  hr.     The  1uotient  is 

104  (the  number 

of  days),  and  18  hr.  remaining. 

Divide  104  da.  by  7  da.     The  quotient  is  14  (the 
number  of  weeks),  and  6  da.  remaining. 

To  avoid  the  appearance  of  a  concrete  quotient 
with  concrete  divisor  and  dividend,  write  da.  and 
wk.  in  parentheses. 

Bring  down  18  hr.  the  first  remainder.     Insert 
the  proper  denominations. 


2.    Change  to  weeks,  days,  and  hours: 

a  1500  hr.        b  2759  hr.        c  1699  hr.        d  2508  hr. 
e  3007  hr.       /  1594  hr.        g  2306  hr.        h  3240  hr. 


182         WALSH'S  BUSINESS  ARITHMETIC 

3.  Change  to  pounds  and  ounces: 

a  375  oz.          b  495  oz.          c  1629  oz.        d  1746  oz. 
e  594  oz.         /  687  oz.          0  2345  oz.        h  3369  oz. 

4.  Change  to  years,  months,  and  days: 

a  1984  da.        6  1763  da.       c  2746  da.       d  1195  da. 
e  3265  da.       /  1429  da.       g  1876  da.       h  2344  da. 

5.  Change  to  bushels,  pecks,  and  quarts: 

a  695  qt.          b  879  qt.          c  1015  qt.        d  1244  qt. 
6  389  qt.         /  467  qt.          g  1137  qt.        h  1878  qt. 

6.  Change  to  yards,  feet,  and  inches: 

a  690  in.          6  798  in.  c  1246  in.         d  1095  in. 

e  587  in.         /  937  in.  g  1315  in.         h  1457  in. 

7.  Change  to  pounds  sterling,  shillings,  and  pence 

a  698  d.  6  884  d.  c  1847  d.  d  2358  d. 

e  987  d.          /  576  d.  g  3015  d.  h  4444  d. 


CHAPTER  FOUR 
SIGNS    AND    OPERATIONS 

The  following  diagram  shows  the  several  arithmet- 
ical operations  with  their  signs,  the  names  of  the  terms, 
etc. 


Operation 

Expression 

16  is  called 
Addend 

2  is  called 

Result  is  called 

Addition 

16  +  2  =  18 

Addend 

Sum 

Subtraction 

16  -  2  =  14 

Minuend 

Subtrahend 

Difference,  or 
Remainder 

Multiplication 

16  X  2  or 
16  •   2  =  32 

Factor,  or 
Multiplicand 

Factor,  or 
Multiplier 

Product 

Division 

16  -*-  2  =  8 

Dividend 

Divisor 

Quotient 

Ratio 

16:2  =  8:1 

Antecedent 

Consequent 

Ratio 

Involution 

162  =  256 

Base 

Exponent 

Power 

Evolution 

^16  =  4 

Base 

Index 

Root 

The  expression  16  X  2  is  read  "16  times  2,"  or  "16 
multiplied  by  2."  When  one  of  the  terms  is  concrete, 
it  is  generally  read  as  the  multiplicand;  thus  $16  X  4 
is  generally  stated  "$16  multiplied  by  4."  A  person 
desiring  to  use  the  word  "times"  reads  it  "4  times  $16," 
regardless  of  the  order  of  the  terms  in  the  expression. 

183 


184         WALSH'S  BUSINESS  ARITHMETIC 

In  arithmetical  subtraction,  the  larger  number  is 
considered  the  minuend  in  such  an  example  as  "Find 
the  difference  between  316  and  500." 

That  16  is  to  be  divided  by  2  may  also  be  indicated 
by  %  or  2)16. 

SIGHT  EXERCISES 

1.  Give  the  value  of  each: 

a  75  +  19  +  25  6  75  +  25  +  19  c  19  +  25  -h  75 

d  25  X  6K  X  4  e  25  X  4  X  &&  f  4  X  6#  X  25 

It  will  be  noted  that  the  values  of  a,  b,  and  c  are  the  same,  showing  that 
addends  may  be  taken  in  any  order;  that  the  values  of  d,  e,  and  /  are  the 
same,  showing  that  factors  may  be  taken  in  any  order. 

2.  Give  the  values  of  the  following: 

a  16%  X  8  X  6  b  12K  X  3%  X  8  c  33%  X  5  X  6 

PRECEDENCE  OF  SIGNS 

It  is  agreed  among  mathematicians  that  when  an 
expression  contains  a  multiplication  (x)  or  a  division 
(-i-)  sign,  and  also  one  of  addition  (+)  or  subtraction 
(— ),  the  product  or  quotient  must  first  be  found. 

Thus,  a  12  X  8  +  2  means  96  +  2 
6  40  +  8  x  2        "      40  +  16 
c  18  -j-  6  -  2        "      3-2 
^  30  -  18  -  9      "      30-2 

To  avoid  misleading  a  person  unacquainted  with 
this  convention,  such  quantities  should  be  placed  in 
a  parenthesis  —  (12  X  8)  +  2 

a  (12  X  8)  -  2  b  40  -  (8  X  2) 

c   (18  •*-  6)  +  2  .  d  30  +  (18  +  9) 


NUMBERS  AND  PROCESSES  185 

A  better  plan  for  the  last  two  would  be  to  write 
them  thus: 

c  *%  +  2  d  30  +  l% 

SIGNS   OF  AGGREGATION 

A  parenthesis  denotes  that  the  value  of  an  expres- 
sion contained  in  it  is  to  be  taken  as  a  whole  in  per- 
forming an  operation. 

A  vinculum,  which  is  a  horizontal  line  over  an  ex- 
pression, has  the  same  meaning  as  a  parenthesis. 

In  dictating  an  expression  containing  a  parenthesis 
or  a  vinculum,  care  must  be  taken  to  avoid  misleading 
the  hearer.  Thus,  it  is  difficult  to  distinguish  between 
(3  X  8)  —  4,  announced  as  3  times  8,  minus  4,  and 
3  X  (8  —  4),  announced  as  three  times,  8  minus  4, 
notwithstanding  the  difference  in  the  pauses. 

A  better  plan  would  be  to  dictate  the  first  "From 
3  times  8,  take  4,"  and  the  second  "3  times  the  differ- 
ence between  8  and  4." 

SIGHT  EXERCISES 

1.  Read  the  following: 

a  (9  X  5)  -  (6  -  3)  -  10  b  24  -  9  -  (24  ^-  4) 

c  9  X  (5  -  3)  -  16  +  (6  -  2)  d  (8  -s-  4)  +  (3  x  5)  -  2 

14  +  10       3  +  7*  8  +  16 

.— ---^  /_±__  +  23-* 

Notice,  in  e  and  /,  the  line  between  two  expressions 
has  the  effect  of  a  vinculum. 

2.  Give  the  value  of  each. 

3.  Which    of  the  foregoing  marks  of   aggregation 
could  be  omitted? 


186          WALSH'S  BUSINESS  ARITHMETIC 

INDICATING   OPERATIONS 
PREPARATORY   EXERCISES 

State  the  operations  needed  to  obtain  each  of  the 
following: 

1.  After  spending  $1.50  for  a  hat,  and  30  cents  for 
a  necktie,  John  has  5  cents  left.     How  much  had  he 
at  first? 

2.  How  much  would  Mary  have  left  out  of  $1.50 
after  spending  30  cents  for  ribbon  and  5  cents  for  pins? 

3.  A  drover  sold  150  sheep  to  one  farmer,  and  30 
sheep  to  another.     How  much  did  he  receive  in  all 
at  $5  a  head? 

4.  How  many  cubic  feet  of  water  are  there  in  a 
rectangular  pond  150  feet  long  and  30  feet  wide  when 
the  water  is  5  feet  deep? 

5.  A  man  had  a  farm  of  150  acres.     How  many 
acres  would  he  have  after  he  had  sold  30  acres  to  Mr. 
A  and  5  acres  to  Mr.  B? 

6.  A  grocer  had  150  pounds  of  sugar.     After  selling 
30  pounds,  he  put  up  the  remainder  in  5-pound  pack- 
ages.    How  many  packages  were  there? 

7.  A  woman  had  $150  in  the  bank.     How  much 
would  she  have  in  the  bank,   exclusive  of  interest, 
after  making  30  weekly  deposits  of  ^5  each? 

8.  At  the  opening  day  of  school  it  had  150  pupils. 
During  the  month  30  pupils  were   admitted,  and  5 
left.     How   many   pupils   belonged   to   the   school   at 
the  end  of  the  month? 

9.  A  planter  raised  150  bales  of  cotton  in  5  fields 
of  30  acres  each.     How  many  bales  did  he  average  to 
the  acre? 


NUMBERS  AND  PROCESSES  187 

10.  Five  children  picked  150  quarts  of  blackberries 
and  30  quarts  of  blueberries.     How  many  quarts  of 
berries  did  each  child  pick  on  the  average? 

11.  A  farmer  had  150  pigs.     He  kept  30  and  sold 
the  others  at  $5  each.     What  did  he  receive  for  those 

he  sold? 

SIGHT  EXERCISES 

Combine  numbers  inclosed  in  a  parenthesis  before 
combining  them  with  the  other  number. 

1.  Give  answers: 

a  150  -h  30  +  5  b  (150  +  30)  +  5  c  150  +  (30  +  5) 

d  150  X  30  X  5  e  (150  X  30)  X  5  /  150  X  (30  X  5) 

2.  What  answers  are  the  same  (a)  in  the  first  line? 
(b)  In  the  second? 

3.  Give  answers: 

a  150  -  30  -  5  6  (150  -  30)  -  5  c  150  -  (30  -  5) 

d  150  -=-  30  -:-  5  e  (150  -=-  30)  -=-5          /  150  ^-  (30  -f-  5) 

4.  What  two  expressions  in  example  3  are  equivalent 
to  each  other  (a)  in  the  first  line?     (b)  In  the  second? 

5.  What    parentheses    could    be    removed   without 
affecting  the  result  in  example  3? 

In  the  following  examples  treat  two  numbers  connected 
by  the  sign  of  multiplication  or  of  division  as  if  they  were 
inclosed  in  a  parenthesis. 

6.  Give  answers: 

a  150  +  30  x  5  b  150  X  30  +  5  c  150  X  (30  -f  5) 

d  (150  +  30)  x  5  e  150  -  30  X  5  /  150  X  30  -  5 

g  150  X  (30  -  5)  h  (150  +  30)  -r-  5  i  150  +  30  -*•  5 

j  150-30+5  k  150  +  (30  +  5)  I  (150  -  30)  X  5 

m  150  -  30  ^  5  n  150  •*-  30  -  5  o  150  -5-  (30  -  5) 

p  (150  -  30)  •*  5  q  150  -  30  -  5  r  150  -  (30  -  5) 


188          WALSH'S  BUSINESS  ARITHMETIC 

When  an  expression  is  composed  of  numbers  con- 
nected by  signs  of  addition  and  subtraction  ( +  and 
— )  exclusively,  the  result  may  be  obtained  by  com- 
mencing at  the  right  and  making  the  combinations  in 
the  order  in  which  they  are  given. 

1.  In  determining  the  value  of  the  expression  20  - 
12+  16—  8  —  4  the  successive  steps  may  be  8  (20  — 
12);  24  (adding  16);  16  (subtracting  8);  12  (sub- 
tracting 4).  Ans.  12. 

The  same  result  is  obtained  when  these  numbers  are 
taken  in  any  other  order,  such  as 

a     20-8-4  +  16-12 
b     16-8-4+20-12 
etc. 

As  an  algebraic  expression  the  order  may  be 

-12-8  +  20-4  +  16 
In  dictating  (1)  say 

20  minus  12  plus  16  minus  8  minus  4 

In  evaluating  an  expression  of  this  kind,  it  is  cus- 
tomary, however,  to  combine  the  addends,  and  from 
their  sum  to  deduct  the  sum  of  the  subtrahends. 

This  may  be  expressed  in  the  following  form: 

20  +  16  -  (12  +  8  +  4) 

the  parenthesis  indicating  that  the  value  of  the  ex- 
pression within  the  parenthesis  is  first  to  be  ascer- 
tained. 

Note  the  change  of  the  signs  prefixed  to  8  and  4 
when  they  are  placed  within  the  parenthesis. 


NUMBERS  AND  PROCESSES  189 

2.  An  expression  containing  numbers  connected  by 
signs  of  multiplication  and  division  ( X  and  -7-  ) 
may  be  evaluated  in  the  same  way.  Thus  in 

16x4-i-8xlO-r-5 

the  successive  steps  may  be 

64  (16  x  4),  8  (dividing  by  8),  80  (multiplying  by  10), 
16  (dividing  by  5).  Ans.  16. 

The  same  result  is  obtained  by  making  the  succes- 
sive operations  in  any  order.  The  following  are 
examples : 

a     16-5-8x10x4-5-5 
b     10  +  8xl6-:-5x4 
etc.,  etc. 

In  practice,  however,  divide  the  product  of  the 
multipliers  by  the  product  of  the  divisors,  thus  , 

c    16  x  10  x  4  +  (8  x  5), 

writing  it  as  shown  below: 

16  x  10  x  4 

d      T^y~ 

Then,  shorten  the  work  by  cancellation. 

Note  the  change  of  the  sign  preceding  the  5  when 
it  is  placed  in  the  parenthesis  in  c  and  below  the  line 
in  d. 


CHAPTER  FIVE 

ADDITION 
COUNTING  EXERCISES 

Count  by  6's,  beginning  (a)  with  6.  (6)  With  7. 
(c)  With  8.  (d)  With  9.  (e)  With  16.  (/)  With  17. 

2.  Count  by  7's,  beginning  (a)  with  7.     (6)  With  8. 
(c)  With  9.    (d)  With  17.    (e)  With  19.    (/)  With  27. 

3.  Count  by  8's,  beginning  (a)  with  8.     (6)  With  9. 
(c)  With  18.     (d)  With  19.    (e)  With  28.    (/)  With  29. 
(0)  With  22.    (A)  With  23. 

4.  Count  by  9's,  beginning  (a)  with  9.    (8)  With  19. 
(c)  With  29.     (d)  With  21.    (*)  With  22.     (/)  With  23. 

(0)  With  24.    (A)  With  25.    (i)  With  26. 

• 

ORAL  DRILLS 

One  type  of  the  daily  "warming-up"  drill  is  a  count- 
ing exercise. 

The  teacher  announces  "Counting  Drill."  The 
class  stands.  A  scorer  at  the  blackboard  records 
the  time.  The  teacher  says  "By  6's."  Successive 
pupils  say  12,  18,  24,  30,  etc.,  each  taking  his  seat  as 
he  answers.  When  102  is  reached,  the  teacher  says 
"7,"  and  the  pupil  whose  turn  it  is  to  answer  says 
"  13,"  and  the  others  continue  20,  27,  etc.  to  103. 

The  scorer's  duty  is  to  call  "time"  at  the  expiration 
of  3  minutes,  and  to  note  the  number  of  combinations 
that  have  been  correctly  made  in  the  period.  Each 

190 


NUMBERS  AND  PROCESSES  191 

result  should  be  compared  with  previous  ones  to  de- 
termine the  rate  of  progress  made  by  the  class  in  rapid 
work. 

SIGHT  DRILLS 

Give  the  total  of  each  column: 

a  66,666  b  77,777  c  88,888  d  99,999 

66,666  77,777  88,888  99,999 

66,666  77,777  88,888  99,999 

66,666  77,777  88,888  99,999 

66,666-  77,777  88,888  99,999 

66,666  77,777  88,888  99,999 

66,666  77,777  88,888  99,999 

66,666  77,777  88,888  99,999 

66,666  77,777  88,888  99,999 

66,666  77,777  88,888  99,999 

66,666  77,777  88,888  99,999 

98,765  56,789  97,586  45,678 

Drills  similar  to  the  foregoing  should  be  written  in 
large  figures  on  manila  paper  for  occasional  use. 

The  foregoing  sight  drills  contain  the  same  combi- 
nations as  occur  in  the  counting  exercises.  The  num- 
bers are>  however,  in  sight,  which  is  of  great  help 
to  many  pupils;  it  is  also  the  way  in  which  most  of 
their  adding  is  done. 

MENTAL  WORK 

Some  drills  should  be  employed  in  which  the  num- 
bers are  not  in  sight.  Answers  to  these  combinations 
may  be  given  orally  by  individuals  at  one  recitation. 
At  another,  answers  may  be  written  by  all  the  pupils. 

1.   Miss   Bollin   spent   $1.67   for   muslins   and 
for  gloves.     Find  the  total. 


192          WALSH'S  BUSINESS  ARITHMETIC 


Think  two,  thirty-seven  (1.67  +  -70);  two,  forty- 
two  (adding  .05).  Give  the  answer  as  two,  forty- 
two. 

If  the  answer  is  to  be  written,  first  write  2  42, 
then  insert  the  decimal  point  and  prefix  the  dollar 
sign. 


2.  Give  sums: 

a    39£  +  46^          6   47^  +  84^  c   $1.59  +  $.33 

d    Mi  +  38£          e    18£  +  96£  f     4.17  +    .67 

g    63^  +  Hi          h   75£  +  S8f*  i     6.36  +    .45 

j    45^  +  Z5t          k   37£  +  63^  I      8.67  +    .28 

m  54^  +  36^          n  95£  +  78^  o     3.78  +    .16 

p    18£  +  68£          q   28^  +  84ff  r     7.45  +    .39 

s    73£  +  19^          t    57^  +  58^  u    5.80  +    .18 

v    81^  +  13^          w  67 'i  +  87^  x     2.28  +    .56 

3.  Carl  Hall  has  two   farms,  one  containing  368 
acres  and  the  other  containing  475  acres.     How  many 
acres  are  there  in  both? 


PROCESS 

Think  768  (368  +  400),  838  (adding  70),  W 
(adding  5).  ^43  A  Ans. 

4.  Give  sums  : 

a  459  +  83 

6  659  +  183 

c  378  +  659 

d  684  +  17 

e  198  -f  247 

/  456  -f-  548 

g  852  +  49 

h  484  +  176 

i  737  4-  837 

j  275  +  29 

k  145  4-  693 

/  295  4-  926 

m  729  +  95 

n  838  +  129 

o  816  4-  495 

p  369  +  38 

q  134  +  568 

r  648  4-  372 

s  546  +  57 

*  356  +  155 

u  189  4-  818 

v  138  +  68 

w  119  +  777 

x  576  4-  654 

NUMBERS  AND  PROCESSES  193 

5.   Edward  traveled  268  miles  on  Monday  and  197 
miles  on  Tuesday.     How  far  did  he  go  in  the  two  days? 


METHOD 

Since  197  is  3  less  than  200,  deduct  3  from  the 
sum  of  200  and  268.  Think  468  (268  +  200), 
465  (subtracting  3).  465  mi.  Ans. 


6.   Give  sums: 

a  347  +  99  b   568  +  399  c  784  +  499 

d  568  +98  e    245  +  698  /  426  +  899 

g  848  +97  h  785  +  197  i  189  +  999 

j  289  +96  k  318  +  596  /  538  +  698 

m  627  +  39  n  609  +  299  o  616  +  597 

p  465  +29  q    177  +  598  r  256  +  898 

s  719  +  59  t    644  +  297  u  838  +  299 

v  153  +49  w  437  +  496  x  347  +  998 

ORAL  PROBLEMS 

1.  Dr.  Bragg  paid  $975  for  a  car  and  $98  for  addi- 
tional equipment.     What  did  he  spend  in  all? 

2.  Find  the  total  amount  of  the  bill  for  a  $75  grapho- 
phone  and  $19  worth  of  records. 

3.  A  farmer  had  last  year  265  acres  in  wheat.     This 
year  his  wheat  acreage  is  69  acres  larger.     How  many 
acres  has  he  in  wheat  this  year? 

4.  Before  the  war  a  certain  grade  of  paper  was  sold 
at  $95  a  ton.     During  the  war  the  price  increased  $38. 
Find  the  later  price. 

5.  A  pile  of  wood  contains  78  cubic  feet  more  than 


194          WALSH'S  BUSINESS  ARITHMETIC 

a  cord,  which  is  128  cubic  feet.     How  many  cubic 
feet  are  there  in  the  pile? 

6.  Newton    is    654    miles   from    Chicago,    and   La 
Junta    is    370    miles    beyond    Newton.     How    far    is 
La  Junta  from  Chicago? 

7.  A  man  has  $675  in  the  bank.     How  much  will  he 
have  in  the  bank  after  he  deposits  $175? 

8.  In    1917   a  man's   salary   was   $1575.     In    1918 
he  was  paid  $250  more.     What  was  his  salary  in  1918? 

9.  A  man  born  in  1843  died  at  the  age  of  69.     In 
what  year  did  he  die? 

10.  The  capacity  of  a  shoe  factory  was  465  pairs 
a  day.     By  better  management  this  was  increased  by 
78  pairs.     What  was  its  later  capacity? 

11.  An   employee  was   paid   a   monthly   salary   of 
$285   and   certain   commissions.     How   much   did  he 
receive  in  all  in  a  month  during  which  his  commission 
amounted  to  $178? 

WRITTEN  EXERCISES 
ADDITION 

1.  A  farmer's  account  book  shows  the  following 
expenses  an  acre  in  connection  with  his  potato  crop: 

Plowing  $3.47  Spray  Material  $1.23 

Fertilizing  6.50  Spraying,  twice  .25 

Disking  1.37  Digging  1.83 

Harrowing  .52  Picking  up  2.70 

Seed  13.12  Sacks  4.05 

Cutting  seed  1.75  Sewing  &  Loading        .45 

Planting  1.05  Transporting  1.35 

1st  Cultivating  .57  Interest  15.— 

Cultivating,  4  times     4.20  Taxes  3.10 


NUMBERS  AND  PROCESSES  195 

a  Find  the  total  expenses  an  acre. 


PROCESS 

$3.47  Write  the  items  in  a  column.     Beginning 

6.50  at   the   bottom,    think    10,    etc.,  ...  61 

1.37  and  write  1,  carrying  6;  think  7,  10,  etc. 

.52  When  the  total  is  found  by  adding  up- 

etc.  ward,  cover  the  answer  with  a  piece  of 

1.35  paper  and  write  on  the  latter  the  column 

4.05  totals  found  by  adding  downward. 

Think  14,  16,  18,  etc. 

Carrying  6,  think  10,  15,  18,  23,  etc. 


Compare  the  two  results.     If  they  agree,   the 
addition  may  be  taken  as  correct. 


In  adding  aloud  follow  a  similar  procedure.  Ignore  the  cipher  in  the 
first  column  (and  in  all  others)  and  announce  10,  the  sum  of  the  first  two 
significant  figures,  without  mentioning  five  and  five.  When  the  final  total 
61  is  announced  write  1  and  carry  6  without  saying  anything  about  it. 
That  6  has  been  carried  is  shown  by  its  combination  with  1  of  the  second 
column  to  make  7. 

NOTE:  Omit  superfluous  words  and  figures. 

b  If  the  gross  receipts  were  $95.20  an  acre,  what 
was  the  profit  on  130  acres? 

c.  What  was  the  value  of  the  land  an  acre  if  the 
rate  of  interest  paid  was  6%? 

2.  The  following  is  an  itemized  statement  of  the 
expense  account  of  Fleming  &  Co.  for  a  month: 

Salaries  $2304.75 

Labor  409.50 

Traveling  expenses  45.83 

Taxes  29.60 


196         WALSH'S  BUSINESS  ARITHMETIC 

Insurance  18.24 

Office  supplies  118.66 

Advertising  265.40 

Telegrams  463.27 

Telephone  245.18 

Postage  295.87 

Light,  heat,  etc.  162.— 

Painting  and  repairs  230. — 

Cartage  56.84 

Rent  375.— 

Miscellaneous  46.89 

What  is  the  total  for  the  month? 

When  the  addends  are  numerous  and  composed  of  large  numbers,  write 
the  total  of  each  column  alongside,  then  write  the  figures  in  the  footing. 
In  checking  the  result  cover  the  side  totals  as  well  as  the  footing.  On  a 
strip  covering  the  side  totals,  write  the  new  ones.  Compare  the  two.  See 
that  the  footing  agrees  with  the  second  set  of  side  totals. 

In  case  of  disagreement  between  two  results,  the  side  totals  render  it 
unnecessary  to  go  back  more  than  a  column  to  make  sure  of  the  number 
to  be  carried  to  the  column  in  which  a  discrepancy  exists. 

3.  Find  sums.  Test  answers.  - 

a  97,864      6  124,756      c  32,785      d  37,694 

7.987  325,675       137,393        82,969 
2,767        39,248       145,358        130,402 

89,574  7,878  72,364  69,735 

32,478  17,669  8,442  77,496 

6,724  347,896  83,739  84,968 

5,978  73,059  321,452  198,695 

86,456  8,877  37,242  6,956 

59,472  56,893  836  92,729 

8,769  6,425  45,878  234,919 

68,245  447  8,384  268,948 

7.988  8,348  48,927  17,963 
47,747  82,720  3,229  25,698 

8,486        53,587        16,279         8,778 

748         2,352       131,832         8,969 

69  178         4,075          576 


NUMBERS  AND  PROCESSES 


197 


e  $6,837.42      /  $53,819.37      g        468.987 

h     5,628.3478 

924.85            16,445.86                 37.5384 

353.68 

6,193.74              2,437.75            1,428.3 

1,753.0809 

33,448.93                 827.54               926.74 

4,736.249 

217.68           54,394.68            8,394.8945 

37,459.08 

437.56                   37.25            7,534.3 

3,485.6052 

5,827.38                 876.34          48,269.057 

4,796.804 

5,672.84              6,786.91            2,736.8052 

6,248.72 

54,984.93                 827.36            8,548.291 

645.0783 

847.62            42,345.89                   3.0787 

486.57 

9,382.49              2,651.48                 65.45 

3,467.343 

3,483.57                 753.43               382.345 

25,895.8 

37,896.82           48,269.27                 37.0006 

28,378.56 

6,438.75            36,854.82               826.623 

243.93 

52,417.24                   91.76            4,327.14 

7,284.075 

432.66              3,824.53            2,557.8346 

762.88 

13.89                 826.62       '   68,349.05 

8,234.9 

4.75            34,327.14            7,654.345 

28,351.0402 

23.64              2,557.83                 23.68 

3.006 

4.   The  following  are  the  receipts  for 

a  week  in  the 

specified  departments  : 

Dry  Goods  Millinery   Notions 

Shoes      Total 

Monday          $1,928.75      $346.42     $289.85 

$358.77       (e) 

Tuesday            1,056.34        275.98       305.64 

323.84       (/) 

Wednesday       1,328.69        304.69       316.38 

336.91       (g) 

Thursday          1,046.78        236.77       337.49 

305.83       (*) 

Friday                  984.67       251.09       250.08 

298.64       (*) 

Saturday           2,345.56       546.57       375.97 

475.86       (j) 

Totals                (a)               (6)             (c) 

(<*)           (*) 

Find  the  total  for  each  department  (a)  to  (d).  For 
each  day,  (e)  to  (j) .  The  grand  total  for  the  week  (k) . 

NOTE:  Check  by  comparing  the  grand  total,  (k),  found  by  adding  the 
daily  totals,  (e)  to  (j),  with  that  found  by  adding  the  department  totals 
(a)  to  (d}. 


198 


WALSH'S  BUSINESS  ARITHMETIC 


5.  From  the  following,  find  the  cost  to  the  govern- 
ment of  the  outfit  of  an  infantry  private  for  clothing 
and  shelter: 


6.25 


1  bedsack 
3  blankets  @ 

1  waist  belt 

2  pr.  breeches  @  4.45 

2  service  coats  "  7.60 
1  hat  cord 

3  pr.  drawers  @     .50 
3    "  "    1.62% 
1    "  gloves 

1  hat 

2  pr.  shoe  laces  @  .02% 
1    "  leggings 


$0.98 

2  flannel  shirts  @ 

$3.64 

.25 

2  pr.  shoes 
5    "   stockings  " 
4  identification 

5.10 
.30 

.08 

tags           @ 
3  undershirts  @ 

.00% 
.50 

4           "           " 

1.22 

1  overcoat 

.61 
1.70 

1.05 

5  tent  pins  @ 
1     "    pole 
1  poncho 
1  shelter  tent 

.04 

14.92 


3.55 
2.95 


6.  Find  the  cost  to  a  midshipman  of  the  following 
articles  with  which  he  must  provide  himself  upon  his 
admission  to  the  Naval  Academy: 

1  box  soap  .30 

1  hair  brush  .65 

stationery  1.75 
12  white  handker- 
chiefs @               .20 

1  pr.  suspenders  .40 
4  suits  pajamas  @  .70 

1  tooth  brush  .18 
thread  and  needles  .75 
brush  and  blacking  .50 
nail  brush  .50 
6  pillow  cases  @  .13 

name  plate  .15 

2  bedspreads  @  1.25 

1  slop  jar  1 . — 

2  spatter  cloths  @  .50 


1  white  cap  and 

anchor 

$2.45 

1  dress  jacket 

20.78 

1  blouse 

15.22 

1  pr.  dress  trousers 

11.83 

1    "service     " 

6.68 

1  overcoat 

26.98 

1  reefer 

12.18 

1  mackintosh 

11.50 

1  cap  cover 

.24 

2  pr.  leggings  @  $.70 

1  parade  cap 

3.10 

1  mug 

.07 

1  soap  box 

.18 

1  laundry  book 

.25 

1  pr.  blankets 

3.75 

NUMBERS  AND  PROCESSES 


199 


1  pair  overshoes  .83 

2  "  high  shoes  @  4.80 
8  white  shirts    "     .50 
12  collars  "     .10 
2  white  blouses  "4.— 
12  pr.  cuffs         "     .18# 
12   "   socks        "     .20 
8  towels              "     .20 

1  shaving  outfit  2.65 

12  pr.  drawers  @  .40 

12  undershirts  @   .36 

1  hand  glass  1.15 

1  blue  sweater  3.15 

2  "     jerseys  @  2. — 

1  pr.  white  shoes  1.80 

1  requisition  book  .40 

1  pass  book  .30 

3  stencils  @  .25 

1  basin  and  pitcher  .90 

1  Pr-  gymnasium 

slippers  .87 

1  whisk  broom  .17 

1  coarse  comb  .12 

7.   Add  horizontally  and 

2,259,969  +  313,225 
30,631,114  +  4,624,231 
15,192,362  +  3,657,641 

1,241,410  +  132,640 
650,599  +  220,299 

2,336,043  +  156,708 
62,997,808  +  8,444,473 
14,070,829  +  1,160,278 
19,380,698  +  1,822,756 
27,796,815  +  6,799,875 


1  hair  pillow  .75 

1  rug  .75 

1  hair  mattress  4.85 

1  broom  .35 

3  khaki  blouses®  1.67 

4  "      shirts     "2.30 

1      "      belt  .17 

1  waste  paper 

basket  .65 

3  white  hats  @       .35 

1  jackknife  .25 

2  lanyards  @          .12 
6  sheets  @  .65 
hammock  clews  .50 
1  pr.  bathing  trunks           .15 

3  pr.  white  gloves  @  .40 

1  trousers  hanger  .30 

6  coat  hangers  @  .06 

1  strong  box  1.60 

1  pr.  ear  protectors  .20 

2  manuals  @  .41% 

1  pr.  collar  anchors  .75 

2  clothes  bags  @  .25 


vertically : 

2,835,546 
67,384,012 
32,702,416 
2,421,798 
1,334,004 
3,271,787 
+  127,914,369 
+  23,466,950 
+  32,610,057 
+  42,621,617 


(d) 
(•) 
(/) 
(?) 
(*) 


(*) 


ffl 


(m)         =  (n) 


200          WALSH'S  BUSINESS  ARITHMETIC 

ADDING  FRACTIONS 
DRILL  EXERCISES 

1.    Give  answers  rapidly. 

a      %       b      %       c      %       d      y2       e      %       f     % 


h      %       i      X       j      %       k      %       I      %        m     %       n 

+%        +  %         +  X         +X         +  X 

p       %      q       V*       r      %       s      %       t       %       u     % 


2.   Give  sums. 

a  6     X       c 


i      %       j      /2       k      %       I      %      m     % 


ORAL  PROBLEMS 

1.   Last  year  a  farmer's  crop   of  wheat  averaged 
bushels  to  the  acre.     This  year's  was  1%  bushels 
greater.     What  is  the  average  to  the  acre  this  year? 


METHOD 
Think  22%  (21%+  1),  22%  (adding  %)      22%  bu.  Ans. 


2.  Before  the  war  copper  brought  12%f  a  pound. 
A  few  months  later  the  price  was  increased  3%£.     What 
was  the  new  price? 

3.  One  pile  of  wood  contained  2%  cords,  another 
contained  1%  cords.     How  much  wood  was  there  in 
the  two  piles? 

4.  Pohick    is    23Ko    miles    from    Seminary.     Falls 


NUMBERS  AND  PROCESSES  201 

Church  is  8%o  miles  farther.     How  far  is  Falls  Church 
from  Seminary? 

5.  Two  pieces  of  silk  contained  18%  and  10%  yards, 
respectively.     How  many  yards  were  there  in  both? 

6.  After  7%  pounds  of  butter  were  sold  from  a  tub 
it  contained  48%  pounds.     How  many  pounds  did  it 
contain  originally? 

7.  A  man  worked   8%  hours   on  Monday   and   7% 
hours  on  Tuesday.     How  many  hours  did  he  work 
on  both  days? 

8.  A   woman  bought   7%  pounds   of   beef   and   3% 
pounds  of  veal.    How  many  pounds  of  both  did  she  buy? 

9.  A  girl's  expenses  for  a  week  were  $8%,  and  her 
savings  were  $2%.     What  did  she  earn? 

10.  The  distance  between  the  first  plant  in  a  row 
and  the  last  is  87  feet.     These  plants  are  each  1%  feet 
from  the  end  of  the  row. 

(a)  How  long  is  the  row?  (6)  How  many  plants 
3  feet  apart  are  there  in  the  row? 

SIGHT  EXERCISES 

When  the  mixed  numbers  are  in  the  view  of  the 
pupils,  those  who  desire  to  begin  the  work  by  adding 
the  fractions  may  be  permitted  to  do  so. 

When  the  answers  to  the  following  are  to  be  written, 
the  result  should  be  obtained  by  the  pupil  before  he 
begins  to  write. 

1.  How  many  acres  are  there  in  two  fields,  one 
containing  40%  acres  and  the  other  containing  7%  acres. 


METHOD 

Think  47%  (40%+  7),  48%  (adding  %).       48%  A.  Ans. 


202          WALSH'S  BUSINESS  ARITHMETIC 

2.   Give  sums: 

a    17%  b    18%  c  19%  d     20% 

+        %  +        %  +       %  +       % 


e     15%  /    16%  0     20%  h     21% 


™    15%  n    16%  o      20% 

+  11% 


i      15%  j     16%  fc      20%  Z 

+  10%  +10%  +10%  +10% 


3.   Give  sums: 

a     10%  b    11%  c    12%  d    13% 


c     20%  /    21%  g    22%  /*    23% 

+   5%  +4%  +5%  +6% 

2      30%  j     31%  &    32%  Z 


m    41%  n    42%  o    43%  p    44% 

<7     52%  r     53%  5    54%  t     55% 


i*     65%  0     64%  w  63%  a;    62% 

+  _!%  +_2%  +_3%  +J% 

WRITTEN   EXERCISES 

In  wholesale  dry-goods  houses  12%  is  written  121, 
is  written  132,  14%  is  written  143,  the  denominator, 
4,  being  omitted. 

1.   Add  the  following.     Write  answers  directly  from 
the  book: 


b    72yd. 

c  312  yd. 

d  II1  yd. 

e    23 

163 

402 

182 

343 

252 

31 

63 

283 

43 

193 

332 

102 

211 

223 

201 

I2 

372 

392 

263 

382 

NUMBERS  AND  PROCESSES  203 

a  141  yd.       b    72  yd.       c  312  yd.       d  II1  yd.       e    23  yd. 

83 
362 

51 
171 

Check  each  result  by  adding  downward,  if  the  first 
result  is  obtained  by  adding  upward. 

In  writing  pounds  and  ounces,  grocers  sometimes  use 
small  figures  to  express  ounces,  writing  the  latter  as  frac- 
tions of  a  pound,  but  omitting  16,  the  denominator. 

2.  Add  the  following,  writing  answers  directly 
from  the  book: 

e    83    Ib. 
1413    " 

31io    « 


a    381  Ib. 

b  2115  Ib. 

c  192    Ib. 

d     614 

2611   " 

225    " 

33     « 

284 

397   " 

208    " 

56     " 

346 

3714  " 

j4       « 

363     " 

189 

913   " 

1Q12     « 

252     " 

4012 

175  " 

339      « 

310    « 

1615 

Fractions   in   business   are   generally   limited   to   halves, 
quarters,  eighths,  sixteenths,  etc. 

3.   Add.     Write  answers  directly  from  the  book. 

a  16%  b  23%  c  25%  d    9% 

8%  9%  42%  18% 

23%  42%  42%  6% 

5%  _6Ke  J%  17M. 

e  23K      /  37%      flf  48%      A  50% 

7%  8%  9%  10% 


8X2 


204          WALSH'S  BUSINESS  ARITHMETIC 

4.   Find  the  total  weight  of  six  pieces  of  meat  weigh- 
ing, respectively,  16^  lb.,  8%  lb.,  9%  lb.,  11%  lb.,  and 
lb. 


16/2  lb. 

8% 

9% 

11% 


Ans.  60%  lb. 


PROCESS 

g  Write  the  addends  in  a  col- 

2  umn  and  draw  a  perpendicular 
4  line  on  the  right  to  separate  the 
Q  new  numerators  from  the  origi- 

3  nal  fractions.      In  the  second 
37   _  QIV  column,    write    16,    the    least 


common  denominator,  on  a  line 
below  the  last  addend  in  the  second  column,  and  write 
over  this  the  sum  of  the  new  numerators  when  found. 
Write  the  new  numerators  alongside  the  corresponding 
fractions.  Write  43,  their  sum,  over  16  previously 
written.  Reduce  %  to  2%.  Write  %  under  the  origi- 
nal fractions,  and  carry  2  to  the  whole  numbers. 

A  Shorter  Method 

• 

A  pupil  that  notes  that  the  sum  of  %  and  %  is  1%,  which 
makes  2  when  united  with  %,  has  left  only  two  fractions 
to  combine,  %  and  %e,  whose  sum  is  %,  which  he  writes. 
He  then  carries  2  to  the  whole  numbers. 

Use  this  method  to  check  the  sum  of  the  fractions. 


In  adding  mixed  numbers  containing  such  fractions,  for 
example,  as  %j,  &  %,  %6,  %,  and  %,  accountants  frequently  re- 
arrange the  addends,  especially  in  testing  a  result,  to  bring 
the  fractions  together  in  this  order:  %,  %;  %$,  %j,  &  %. 

Even  when  combinations  making  1  are  not  possible,  as 
in  &  %,  %,  %,  %,  %,  they  rearrange  the  addends  in  some  such 
way  as  this:  %,  %,%;%,  %>  %',  combining  the  first  three 
mentally  into  %  or  2^,  and  the  next  three  into  %  or 
etc. 


NUMBERS  AND  PROCESSES  205 

5.  Add: 

a  S6&             b  28%              c  86%  d  125% 

8%                   86%                     8%  20% 

93%                     7%s                  95%  354% 

27%                  20%                     5&  68% 

45%                     9%                  66%  98% 

8%                   5.3%                     8%  7% 

6.  Find  the  sum   of  3%  days,  5%  days,  7%  days, 
9%  days,  11%  days,  13&  days. 


PROCESS 

In  finding  the  least  common  multiple  of  the 
denominators  of  these  fractions,  omit  from  con- 
sideration 2,  which  is  a  factor  of  4;  3,  a  factor  of 
6;  4,  a  factor  of  8;  6,  a  factor  of  12.  Find  the 
least  common  multiple  of  8  and  12,  by  considering 
multiples  of  12,  beginning  with  24.  As  this  is  a 
multiple  of  8,  it  is  the  least  common  denominator. 


7.  Add  the  following: 

a    5%  b  75%  c  33%  d  432% 

7%                      9%  80%  83% 

9%                    23%  %  157& 

11%                      8%,  36%  28% 

13%                    13%  5%  7% 

8%6  29%  18% 


8.  A  person  made  purchases  of  pencils  as  follows: 
2%  gross,  3%  gross,  %  gross,  8%  gross,  %  gross,  and  9%a 
gross.  How  many  gross  did  he  buy  in  all? 


206          WALSH'S  BUSINESS  ARITHMETIC 


gross 


177       « 


PROCESS 

After  rejecting  denominators  that 
are  multiples  of  others,  there  remain 
the  following: 

4)  8  -  9  -  12 
2-9- 


/„  L.  C.  M.  =  4  X  2  X  9  =  72 

If  you  do  not  notice  that  8  and  9  are  prime  to 
each  other,  which  makes  72  their  least  common 
multiple,  and  that  72  is  also  a  multiple  of  12,  find 
the  least  common  multiple  of  8,  9,  and  12  by 
writing  these  numbers  in  a  line.  Then  divide  by 
4,  which  is  a  common  factor  of  8  and  12.  Write 
under  8  and  12  then*  quotients,  bringing  down  9. 
Cancel  3,  which  is  a  factor  of  9. 

Since  2  and  9,  the  remaining  numbers,  are  prime 
to  each  other;  that  is,  since  they  have  no  common 
factor,    multiply  their   product   by  the    divisor  4, 
which  gives  72,  the  least  common  multiple. 


9.  How  many  pens  are  there  in  2K  gross,  4%  gross, 
v/t  gross,  X  gross,  5%  gross,  IX   gross,  3#6  gross,  7#s 
gross,  %4  gross,  9X6  gross,  and  8#2  gross? 

10.  Add  the  following: 


a  18&  b    6X  c  22%  d  125%, 

9%4  27%  5%  14X 

16X  85%  16X  8% 

%  8#  30%  Xo 

20%  26%  8%  27% 


NUMBERS  AND  PROCESSES  207 

11.  (a)  Express  in  years  and  a  fraction  the  sum  of  % 
year,  %  year,  %  year,  %o  year,  and  fa  year.     (6)  Change 
each  to  days  (taking  360  days  to  year),  and  find  their 
sum. 

12.  A  machine  consists  of  four  parts,   which   are 
manufactured    from    steel    "blooms,"    weighing    290 
pounds  each.     A  bloom  will  make  either  7  of  one  part, 
9  of  the  second,  20  of  the  third,  or  25  of  the  fourth. 
(a)  Express  the  weight  of  each  part  as  a  mixed  num- 
ber, and  find  their  sum.     (6)  Express  each  as  a  mixed 
decimal  and  find  their  sum.     (c)  Change  the  fractional 
part  of  (a)  to  a  2-place  decimal. 


PROCESS 

41%  Ib. 

Since  there  is  no  factor 

41.4286  Ib 

32%  " 

common  to  any  two   of 

32.2222    " 

14%  " 

the     denominators     the 

14.5 

11%  " 

L.  C.  D.  is  their  continued 

11.6 

Ib. 

/  ,    product,  x  X  &  X  7  X  y 

/  630 

13.    (a)  Find  the  sum  of  IK,  2%,  3%,  4%,  5%,  6%, 
and  9Ko. 


PROCESS 

Find  the  least  common  multiple  of  6,  7,  8,  9  and 
10,  rejecting  the  others. 


(b)  Give  the  answer  as  a  mixed  decimal,  two  places- 

(c)  Change  the    fractions    to    four-place    decimals, 


208          WALSH'S  BUSINESS  ARITHMETIC 

add  the  numbers  as  mixed  decimals,  and  express  the 
result  as  a  mixed  two-place  decimal. 


PROCESS 

\%  .5 

%  .3333  Write  the  decimal  equivalent  along- 

etc.  etc.  side.    Increase  the  fourth  place  of  the 

5%  .1667  decimal  equivalent  of  %  and  of  y,  since 

6)7  .1429  the  next  figure  in  each  is  greater  than  5. 

etc.  etc. 


17.  Add  the  following,  changing  the  fractions  to 
decimals.  Give  answer  as  a  mixed  decimal. 

1%  +  %%  +  3%  +  4%  +  5%  +  6%  +  7%  +  8%  +  9%0 

ADDING   COMPOUND   NUMBERS 
SIGHT  EXERCISES 

1.  How  many  pounds  and  ounces  are  there  in  two 
pieces  of  meat,  one  of  which  weighs  5  pounds  10  ounces 
and  the  other  3  pounds  8  ounces? 


METHOD 


Think  8  Ib.  10  oz.  (5lb.  10  oz.  +  3  lb.), 
8  lb.  18  oz.  (adding  8  oz.),  9  lb.  2  oz.  (reducing) 

Ans.  9  lb.  2  oz. 


2.   Add: 

a       3  lb.  10  oz.  b      4  lb.  9  oz.  c      6  lb.  10  oz. 

+2  lb.    6  oz.  +4  lb.  9  oz.  +2  lb.  11  oz. 


NUMBERS  AND  PROCESSES  209 

d       4  yd.  2  ft.  e      5  yd.  2  ft.  /      9  yd.  1  ft. 
+3  yd.  1  ft.                   +6  yd.  2  ft.  +7  yd.  1  ft. 

g       6  gal.  1  qt.  h     7  gal.  1  qt.  i     8  gal.  3  qt. 
+2  gal.  2  qt.                 +3  gal.  3  qt.  +1  gal.  3  qt. 

j        4  bu.  2  pk.  fc     5  bu.  2  pk.  I      3  bu.  2  pk. 

+4  bu.  2  pk.  -f  3  bu.  3  pk.  +2  bu.  3  pk. 

??i      £5  10s  n      £8  12s  o      £6  18s 
+£6  10s                          +£9  12s  +£2  10s 

p       6  ft.  3  in.  g      8  ft.  10  in.  r      9  ft.  8  in. 
+4  ft.  9  in.                     +1  ft.  10  in.  +2  ft.  7  in. 


WRITTEN  EXERCISES 

Add  the  following.     Write  answers  from  the  book 

a  £24  16s    3d  b  32  yd.  1  ft.  10  in. 

896  526 

15  10    10  18         1         7 


c  16  gal.  2  qt.  1  pt.  d    62  bu.  1  pk.  6  qt. 
35          3  534 

911  24         2 

41  613 


e  43  Ib.  8  oz.   /  8  ft.  10  in.   g  2  mi.  90  rd. 

18   10       63    5       10    120 

65        89        3     84 


CHAPTER  SIX 

SUBTRACTION 

PREPARATORY  EXERCISES 

MAKING  CHANGE 

1.   What  change  does  a  clerk  hand  a  person  who 
gives  a  $20  bill  to  pay  for  articles  amounting  to  $16.85? 


METHOD 

The  clerk  hands  a  nickel,  saying  "sixteen, 
ninety";  a  dime,  saying  "seventeen  dollars"; 
a  dollar,  saying  "eighteen  dollars";  and  a  2-dollar 
bill,  saying  "twenty  dollars." 

He  gives  5{  +  10^  +  $1  +  $2  =  $3.15 


2.  State  the  denominations  of  the  money  used  to 
make  change  from  $1  tendered  in  payment  for  pur- 
chases amounting  to  the  sum  specified  below.  State 
also,  in  each  case,  the  total  amount  given  in  change. 


a  Si  b  76t          c    S9t          d  45ff  e 

f  It  g  ISt  h    Sit  i   Mf          j 

k  4  I  94^  m  6ty          n 


WRITTEN  EXERCISES 

1.   A  man  earned  $1800  during  the  year.     He  spent 
$1475.35.     How  much  did  he  save? 

210 


NUMBERS  AND  PROCESSES  211 


PROCESS 

$1800.—  To  subtract,  begin  with  1475.35 

-  1475.35  (the  subtrahend).    Think  5  and  5 

$324.65  Ans.     (writing     5)     are     10.       Think  4 

(carrying  1)   and  6  (writing  6)  are  10.     Think  6 

(carrying  1)   and  4  (writing  4)  are  10.     Think  8 

(carrying   1)  and  2  (writing  2)  are  10.     Think  5 

(carrying  1)  and  3  (writing  3)  are  8. 

CHECK 

Cover  $1800  (the  minuend)  and  add  $324.65  (the 
remainder)  to  $1475.35. 


2.  Find  remainders.    Check. 

a  345.1                     b   473  c  1016.82 

-    57.064                 -  389.49  -    893.9 

3.  Subtract  without  rearranging. 

a  -  29.86                    b  -  146.5  c  -  383.47 

157.328                          212.17  1000. 

d  $9245.18                   e      16,059  /  -  764.58 

-  264.83                        -   1,088  1113.2 

g  -  $321.69                 h  10,193.8  i       12,657 

1523.07                  -      654.95  -   9,879 

j       101,087                  k  -93,847  I   $1364.57 

-  65,564                         104,305  -     890.09 

m  -  172,654                 n  -  18.25975  o   293,647 

200,001                       106.0005  -  188,898 

4.  The  following  is  a   statement  of  Mr.   Fallen's 
account  with  Gaston  and  Carroll  at  the  close  of  busi- 
ness Jul.  31,  1920. 


WALSH'S  BUSINESS  ARITHMETIC 

MR.  C.  FALLEN  TUCSON,  ARIZ.,  Aug.  1,  1920 

2562  Georgetown  Boulevard 

In  Account  with  G ASTON  and  CARROLL 


Jul. 

6 

To  Mdse. 

273 

46 

9 

58 

95 

11 

187 

84 

15 

36 

92 

18 

375 

14 

20 

263 

88 

29 

« 

95 

44 

(«) 

Cr. 

Jul. 

12 

By  Mdse. 

256 

40 

18 

"    Cash 

100 

22 

"   Mdse. 

310 

89 

29 

«        « 

63 

75 

30 

"   Cash 

100 

— 

(6) 

Bala 

nee  d 

ue 

(<0 

Copy  the  foregoing  statement  inserting  at  (a)  the 
sum  of  the  debits,  at  (6)  the  sum  of  the  credits,  and  at 
(c)  the  balance  due  Gaston  and  Carroll. 

5.  A  farmer's  receipts  and  expenditures,  respec- 
tively, for  the  year  are  shown  in  the  following  table: 


Receipts           Expenditures       Balance 

January 

$187.43 

$138.98 

= 

$48.45 

February 

156.14 

125.47 

= 

w 

March 

195.80 

156  — 

= 

(d) 

April 

163.44 

135.29 

= 

(e) 

May 

201.59 

163.88 

= 

(/) 

June 

198.65 

148.77 

= 

(d) 

July 

302.88 

205.93 

• 

w 

August 

356.<).'5 

216.84 

= 

(i) 

September 

298.67 

225.98 

= 

(j) 

October 

215.42 

160.56 

= 

(*) 

November 

198.68 

123.15 

• 

0) 

December 

125.94 

112.68 

= 

(*) 

Totals 

(a) 

(b) 

= 

(n) 

NUMBERS  AND   PROCESSES  213 

Find  (a)  his  receipts  for  the  year.  (6)  His  expendi- 
tures. (c  to  m)  His  monthly  balances,  (n)  The 
balance  at  the  end  of  the  year. 

Find  (n)  by  adding  the  last  column.  Check  by 
covering  (n)  and  writing  on  the  paper  the  difference 
between  (a)  and  (b). 

ORAL  DRILLS 

1.  Anna  had  85^.  How  much  will  she  have  after 
spending 


From  S5i  take  40^f,  then  take  9^f. 

Do  not  follow  the  method  used  in  your  Written  Exercises  in  subtraction. 

2.  Give  remainders. 

a  65  -  27  6  91  -  62  c  84  -  36  d  73  -  56 
e  54  -  16  /  86  -  47  0  70  -  29  h  82  -  17 
i  93-65  j  40-24  k  52  -  18  I  63  -  24 

3.  Miss  Bruen  paid  $3.42  for  muslin  and  gloves. 
The  gloves  cost  $1.75.     What  did  the  muslin  cost? 

Think  $2.  42  (deducting  $1),  $1.72  (deducting  70$,  $1.67  (deducting 
5$.     Ans.,  $1.67 

4.  Give  remainders: 

a  121  -  75  b  190  -  175  c  253  -  164 

,   d  137  -  94  e  183  -  116  /  270  -  195 

g  110  -  26  h  174  -  138  i  265  -  187 

j  142  -  88  k  162  -  125  I  210  -  173 

m  246  -  77  n  395  -  316  o  321  -  135 

p  315  -  68  q  572  -  544  r  432  -  146 

s  420  -  37  t  783  -  717  u  511  -  154 

v  511  -  54  w  964  -  909  x  613  -  165 

6.  From  a  crop  of  1216  bushels  of  corn,  Mr.  Popkins 
sold  658  bushels.  How  many  bushels  has  he  left? 

Think  six,  sixteen  (deducting  six  hundred)  ;   five,  sixty-six    (deducting 
fifty)  ;  five,  fifty-eight  (deducting  8).     Ans.  558  bu. 


214          WALSH'S  BUSINESS  ARITHMETIC 
COMBINING  ADDITION  AND   SUBTRACTION 
WRITTEN  EXERCISES 

1.  A  dealer  had  1000  bushels  of  oats.  How  many 
bushels  would  he  have  after  he  had  sold  154  bushels, 
368  bushels,  and  87  bushels? 


PROCESS 
From  1000  bu.         Beginning  with  the  last  subtra- 


154    «       hend,  think   15    (7+8),  19    (add- 
Take    368    "       ing  4),  and  1  (writing  1)  are  20. 
87    "       Think  10  (carrying  2),  16  (adding 
Ans.      391    "       6)>  21  (adding  5),  and  9  (writing  9) 
are  30.     Think  6   (carrying  3)   7 
(adding  1),  and  3  (writing  3)  are  10. 

CHECK 

Cover  1000  with  a  piece  of  paper.     On  this  write 
the  sum  of  391  and  the  three  subtrahends. 


2.  Write  answers  to  the  following  directly  from  the 
book. 

(a)  (6)  (c)                   (d) 

From         1000  1234  3256  5167 

159  216  1038                   369 

Take             87  157  887  2588 

355  99  95  1269 

3.  Give  the  value  of  each  of  the  following: 

a  756  -  (184  +  95  +  367)  d  4430  -  (1234  +  345  +  68) 
6  1239  -  (257  +  388  +  86)  e  3754  -  (2345  +  456  +  77) 
c  2000  -  (1234  +  277  +  95)  /  5473  -  (3456  +  567  +  84) 


NUMBERS  AND  PROCESSES  215 

4.   Write  answers  to  the  following  directly  from  the 
book  or  blackboard : 

a  $10.50  -  ($2.75  +  $.89  +  $3.—) 
b  26.43  -  (  9.50  +  .75  +  1.28) 
c  35.19  -  (  7.63  +  .67  +  2.29) 
d  43.26  -  (  8.79  +  .93  +  3.14) 
e  50.20  -  (  6.28  +  .52  +  5.67) 

6.   Supply  missing  items  (a)  to  (i): 

$137.86  +    $75.93  +  $288.79  =  (e) 

(a)    +    168.76  +      45.63  =  (/) 

289.65  +         (b)     +    195.84  =  (g) 

48.76  +    253.92  +          (c)  =  (h) 

123.45  +      88.87  +    216.77  =  (i) 

$819.30  +  $916.—  +  $989.98  =  (d) 

6.  A  merchant's  cash  account  shows  the  following 
receipts  and  payments  for  eleven  months,  and  the 

totals  for  the  year. 

\ 

Receipts  Payments  Balance 

January             $4,748.56  $3,949.82  $798.74 

February             4,294.87  3,870.89  (a) 

March                 4,655.18  4,327.65  (b) 

April                    4,693.25  4,784.57  (c) 

May                     4,705.93  4,259.85  (d) 

June                     4,456.88  4,078.68  (e) 

July                     4,327.65  3,963.26  (/) 

August                4,278.58  3,859.85  (g) 

September          4,683.95  3,965.78  (h) 

October               4,727.53  4,218.65  (i) 

November           4,515.78  3,887.79  (j) 

December                 (k)  (I)  (m) 

$54,837.63  $48,684.13  (n) 


216          WALSH'S  BUSINESS  ARITHMETIC 

Find  the  balances  for  the  eleven  months  (a)  to  (j) , 
the  receipts  for  December  (&),  the  payments  for 
December  (/),  December's  balance  (m),  the  balance 
at  the  end  of  the  year  (ri). 

The  following  table  shows  the  sums  appropriated 
for  a  year  for  the  specified  items,  also  the  expenditures 
for  %  year: 

Items  Appropriations      Expenditures      Balance 

remaining 

Telephone  $150  80.25  (a)  A 

Repairs  1600  1267.80  (b)  B 

Equipment  1500  1350.—  (c)  C 

Supplies  Manual  Training       600         244.68  (d)  D 

Janitors'  Supplies  500         366.90  (e)  E 

Domestic  Science  Supplies      400        241.40  (/)  F 

Printing  500         317.10  (g)  G 

Water,  Light,  Gas  550        239.80  (h)  H 

Fuel  2075         726.25  (i)  I 

Books  500         434.60  (j)  J 

Helpers  1000        441.52  (k)  K 

Janitors'  Salaries  4000  2114.—  (I)  L 

Drawing  Supplies  350         173.95  (ra)  M 

Athletics  300        274.56  (n)  N 

Miscellaneous  1525         969.90  (o)  O 

Science  Supplies  800        507.36  (p)  P 

Incidentals  250         184.62  (q)  Q 

Music  300         105.30  (r)_  R^ 

I  II  III  IV 

I.  Find  the  total  amount  appropriated.  II.  The 
expenditures.  III.  The  balance  remaining  of  each 
appropriation,  (a)  to  (r).  IV.  The  per  cent  each 
balance  is  of  the  sum  appropriated,  (A  to  R).  (Carry 
out  to  two  decimal  places.) 


NUMBERS  AND  PROCESSES  217 

TAKING  ONE  NUMBER  FROM  THE  SUM  OF  TWO   OR 
MORE  NUMBERS 

PREPARATORY  EXERCISES 

1.   A  boy  who  had  $1.75  earned  50  cents  and  spent 
98  cents.     How  much  had  he  then? 


METHOD 

$1.75 

+  .50  His  balance  is  found  by  taking  $1 

-  1.—  from  the  sum  of  $1.75  and  $0.50, 

+  .02  and  adding  2f£  to  the  remainder. 

$1.27  Ans.  ~ 

«pl.  / O 

In  practice  the  $1  is  not  written,  -50 

but  the  deduction  is  made  neverthe- 
less. $1.27 


THE   COMPLEMENT   OF  A  NUMBER 

The  2  thus  added  is  called  the  complement  of  98,. 
the  complement  of  a  number  being  the  difference 
between  it  and  a  unit  of  the  next  higher  order. 

Thus,  the  complement  of  9  is  1  (10  minus  9),  of  79 
is  21  (100  minus  79),  of  675  is  325  (1000  minus  675). 

To  find  the  complement  of  783.951  take  7,  8,  3,  9  and 
5  from  9;  and  1  from  10,  writing  the  successive  remain- 
ders from  left  to  right. 

2.  A  girl  who  had  $1.75  received  50^  from  her  aunt, 
and  then  spent  $1.88.  How  much  had  she  left? 


218          WALSH'S  BUSINESS  ARITHMETIC 


METHOD 

$1.75  Use   the   complement   of   $1.88, 

.50  which    is    $8.12.     Add    the    three 

8.12  numbers.     Before  writing  the  total 

$         Ans.  °f  the  last  column,  deduct  $10. 


WRITTEN  EXERCISES 


1.  At  the  beginning  of  work  in  the  morning,  the 
factory  had  on  hand  475  tons  of  steel.  During  the 
day  350  tons  were  made  and  587  tons  were  sold.  How 
many  tons  remained? 


PROCESS 

475  T  Write  the  subtrahend  in  the  regu- 

+  350  "          lar    way,   but   use    its   complement, 

'  587<< 


Think  3  (10  -  7),  8  (adding  5);  write  8. 
Think  1  (9  -  8),  6  (adding  5),  13  (adding  7)  ;  write  3. 
Think  4  (9  -  5),  5  (carrying  1),  8  .(adding  3)  12 
(adding  4)  ;  write  2,  omitting  the  1. 


2.  There  were  in  a  warehouse  on  Monday  morning 
649  barrels  of  flour.  During  the  week  488  barrels 
were  received  and  574  were  withdrawn.  How  many 
remained  in  the  warehouse  at  the  end  of  the  week? 


NUMBERS  AND  PROCESSES  219 


PROCESS 

649  bbl.  Write  574  bbl.  but  use  its  comple- 

+  488    "         ment,  426.     Begin  at  the  bottom  so 
—  574  that  you  will  be  less  likely  to  over- 

look the  fact  that  you  are  dealing 
with  the  complement. 


3.   Give  the  value  of  746  -f  184  +  95  -  367. 


PROCESS 

Beginning  with  367,  and  using  its  complement, 
think  3  (10  -  7),  8,  12,  18;  write  8.  Carrying  1, 
think  4  (adding  the  complement,  9  -  6),  13,  21,  25; 
write  5.  Carrying  2,  think  8  (adding  the  comple- 
ment, 9  -  3),  9,  16;  write  6.  Omit  the  1.  Ans. 
658. 


4.  Write  the  answers  to  the  following  directly  from 
the  book  or  the  blackboard. 

a  $4.50  +  $2.75  -  $1.89.  g  3217  +  3087  +  234  -  3628. 

b  $12.60  +  $8.50  -  $10.89.  h  4382  +  2342  +  689  -  1367. 

c  1875  +  387  +  96  -  448.  i  3562  +  4056  +  408  -  6924. 

d  2015  +  86  +  250  -  1234.  j  2341  +  6027  +  824  -  5833. 

e  1887  +  2460  +  329  -  2563.  k  1766  +  5150  +  569  -  3426. 

/  2065  +  1265  +  157  -  4257.  I    2598  +  3006  +  736  -  4762. 

WRITTEN  EXERCISES 

The  following  is  a  statement  of  the  exports  and 
imports  of  each  business  day  for  three  weeks,  begin- 
ning Jul.  17. 


220         WALSH'S  BUSINESS  ARITHMETIC 

Copy  this  statement,  and  complete  it  by  inserting 
for  each  day  its  excess  (a)  of  exports  or  (6)  of  imports, 
(c)  the  total  exports  for  three  weeks,  (d)  the  total  im- 
ports, and  (e)  the  net  excess  of  the  exports. 


Exports 

Imports 

Excess  Exports     Excess  Imports 

Jul. 

17 

7,728,468 

4,601,395 

3,127,073 

18 

12,558,896 

2,902,051 

etc. 

19 

8,440,177 

4,322,549 

(a) 

20 

8,701,825 

2,751,883 

21 

6,263,634 

2,394,123 

22 

9,172,369 

839,442 

24 

10,748,034 

5,472,260 

25 

10,082,167 

5,048,748 

26 

3,568,542 

3,711,062 

142,520 

27 

1,043,375 

2,800,355 

etc. 

28 

1,964,560 

4,385,087 

(b) 

29 

4,865,135 

3,704,030 

31 

8,815,609 

3,791,273 

Aug. 

1 

20,128,921 

5,864,208 

2 

14,178,438 

4,503,504 

3 

6,580,265 

6,776,233 

4 

5,271,135 

5,105,781 

5 

1,471,401 

2,737,628 

Totals  (c)  (d)  (e) 

GROSS  WEIGHT,  TARE,   NET  WEIGHT 

The  gross  weight  of  merchandise  includes  the 
weight  of  the  barrel,  tub,  wagon,  etc.  The  tare  is  the 
weight  of  the  covering,  wagon,  etc.  The  net  weighty 
which  is  the  difference  between  the  two  former,  is  the 
weight  of  the  merchandise. 

The  buyer  weighs  the  packages  when  he  receives 
them  and  compares  the  weight  of  each  with  that 
marked  on  the  package.  When  the  package  is  emptied, 


NUMBERS  AND  PROCESSES  221 

he  weighs  it  and  compares  the  weight  with  the  marked 
one. 

1.  Find  (a)  the  total  gross  weight.     (b)  The  tare. 
(c)  The  total  net  weight  of   the  following   purchase 
of  sugar,  15  barrels. 

327  -  20  336  -  18  340  -  21  335  -  17  339  -  20 
332  -  18  332  -  19  337  -  19  336  -  18  340  -  21 
327  -  17  330  -  19  331  -  18  329  -  17  328  -  17 

2.  The   following   are  the  gross   weights   and   the 
tares  of  12  tubs  of  lard.     Find   (a)   the  total  gross 
weight,  (b)  the  total  tare,  and  (c)  the  total  net  weight. 

74  -  15  70  -  14  71  -  16  60  -  13  70  -  15  68  -  13 
68  -  13  71  -  14  70  -  15  72  -  16  73  -  14  69  -  14 

3.  From  the  following  data  find  (a)  the  total  gross, 
(b)  the  total  tare,  (c)  the  total  net  of  18  loads  of  coal, 
and  (d)  its  value  at  $7.50  a  ton  of  2000  pounds. 

Gross  Tare  Gross  Tare  Gross  Tare 

4764  1236  4756  1216  4912  1248 

4588  1232  4972  1232  4636  1272 

4648  1240  4568  1244  4592  1284 

4720  1248  4884  1312  4756  1268 

4936  1264  4728  1296  4872  1236 

4652  1256  4632  1272  4928  1308 

In  the  vicinity  of  a  market  to  which  farmers  bring 
their  produce,  there  is  generally  a  public  scale  in 
charge  of  a  sworn  weigher.  When  a  farmer  sells  a 
load  of  hay,  he  drives  it  on  the  scales.  The  weigher 
enters  the  weight  of  the  load  and  wagon,  and  when 


222          WALSH'S  BUSINESS  ARITHISIETIC 

the  hay  is  removed,  he  weighs  the  wagon.     To  the 
farmer  he  gives  a  statement  in  the  following  form: 


CERTIFICATE   OF  WEIGHT 


Lawrence,  Michigan,  Aug.  30,  1920 

LOAD  OF. 

.  .Hay  • 

GROSS  WEIGHT  ....  3250  Ib.  . 

OWNER.  . 

.  John  Ziegler 

TARE         "        1130  "  . 

.  .  . 

SOLD  TO 

D  wight  Braman 

NET           "        2120  "  . 

Samuel  Goldstone 

City  Weigher. 

4.  Find  the  value  of  the  foregoing  load  of  hay  at 
$1.35  a  hundred  pounds. 

5.  During  the  day  Mr.  Goldstone  issued  certificates 
for  loads  of  hay  weighing  as  follows.     Find  the  value 
of  each  at  the  price  specified. 

Gross  Tare  Rate  per  100  Gross  Tare  Rate  per  100 

a  3325  1165         $1.25  b  3575  1525         $1.40 

c  3430  1210         $1.30  d  3360  1240         $1.35 

e  3245  1085         $1.15  /  3410  1150         $1.20 

SUBTRACTING  FRACTIONS 
DRILL  EXERCISES 

1.   Give  answers  rapidly: 

a  %          b  %          c   %          d  %          e  %         f  %         g  % 
-X        -X        -%        -X        -X        -X        -X 

h  %          i   %         j   K          k  %          I    %          mX         n  % 
-%        -X        -%         -X        -X        -X        -X 


NUMBERS  AND  PROCESSES  223 

2.  Give  remainders: 

al           b   I           c   1           d  I           el          f  1  g  I 

-_/2        -J4       -_X       -_X       -J       -_X  -_% 

A  1%        i    IX        j   IX        fc  1«        Z    1%        m  1%  n  1% 

-J        -_X       -_K        -_X        -_%       -_ti  -% 

o   1%        p   VA         q    IK         f    1%         5   l/2         «    IX  w  l/6 

-_^     -J     -_%       5%     -_%     -_^  -_x 

3.  (a)  From  1%  take%.     (6)  From  1%  take  %. 


METHOD 

(a)  Think  &  (1  -  %),  %  (adding  %).     Ans.  %. 
(6)  Think  Ks   (1  -  %),  !Ks  (adding  %).      Reduce 

%to%.     Ans.  %. 


4.   Subtract : 

a  1%        6       1%  c    1 


/  1%         <7       1%  fc     1%  i    1%  j   1% 


WRITTEN  EXERCISES 

1.  A  dealer's  stock  of  buttons  at  the  beginning  of 
the  week  was  905%  gross;  at  the  end  of  the  week  it  was 
356%  gross.  If  none  were  bought  during  the  week, 
how  many  gross  were  sold? 


224          WALSH'S  BUSINESS  ARITHMETIC 


A   LONG   METHOD 


905  %    gross 

356% 


548%     gross 


4 
13 


22        After  writing  the  numbers 
and  drawing  the  vertical  line, 
=  y2    as   in    addition,   write   18   as 


the  denominator  of  the  frac- 
tion in  the  remainder,  it  being  the  L.  C.  I),  of  the 
other  fractions.  Change  %  to  fa  writing  4,  the 
new  numerator,  to  the  right  of  the  vertical  line. 
Write  13,  the  numerator  of  the  fraction  in  the  sub- 
trahend, under  9.  Since  %  is  greater  than  fa, 
increase  the  latter  by  %,  writing  22,  the  increased 
numerator,  to  the  right  of  the  4.  Subtracting  13 
from  22,  write  9  over  18,  making  the  fraction  %8 
and  reduce  it  to  J£.  Write  %  under  the  original  frac- 
tions, increase  356  by  1,  and  complete  the  work. 


NOTE:  The  foregoing  method  gives  all  of  the  steps.    The  pupil  should 
omit  as  many  of  them  as  possible. 

2.   Write  answers  from  the  book  if  possible: 

a  192}£  b   385%  c   270%  d  452% 

-    29%  -137%  - 


e   563%  /  771%  g  682%,  h  843% 

-338%  -    97%  -129%  -    65% 

3.   Subtract: 

a  158%  b  862%  c  329%  d  613% 

-  99%  -  593%  -  98%  -  267% 

e  261%  /  706%  g  510#  h  432% 

-  104%  -  69%  -  238%  -    75%, 


NUMBERS  AND   PROCESSES  225 

SIGHT  EXERCISES 

1.   From  a  field  of  48%  acres,  7%  acres  are  sold.     How 
many  acres  are  left? 


PROCESS 


Think  41%  acres  (48%  -  7),  40%  (deducting  %). 
Ans.  40%  A. 


2.   Give  remainders: 

a  20%  6   16%  c   20%  d  17% 


e  20% 
-19% 

/  17% 
-16% 

9  21% 

-20% 

h  18% 

-17% 

i  20% 
-  9% 

3  18% 

-_9% 

k  31% 
-_9% 

/  40% 
-J# 

m20% 
-16% 

n  18% 

-12% 

o  31% 

-25% 

p  40% 

-30% 

ORAL  PROBLEMS 

1.   Last  year  a  farmer's  crop  of  wheat  averaged 
bushels  to  the  acre.     This  year  it  averaged  22%  bushels 
What  is  the  increase? 


PROCESS 


Think  1%  (22%  -  21),  1%  (deducting  %). 
Ans.  1%  bu. 


226          WALSH'S  BUSINESS  ARITHMETIC 

2.  Since  the  war  copper  has  been  sold  at  15%  a 
pound,   an   increase  of  3%^.     What  was  the  former 
price? 

3.  Two  piles  of  wood. contain  4%  cords.     One  con- 
tains 2%  cords;    how  many  cords  does  the  other  con- 
tain? 

4.  A  man  starts  for  Falls  Church,  32  miles  away. 
How  far  has  he  to  go  after  traveling  23Ko  miles? 

5.  From   a   piece    of    cloth   containing    41%    yards 
18%  yards  were  sold.     How  many  yards  remain? 

6.  A  tub  of  butter  weighs,  with  the  tub,  56  pounds. 
The  tub  weighs  7%  pounds.     WTiat  is  the  weight  of 
the  butter? 

7.  A  man  worked  on  Monday  8%  hours,  on  Tuesday 
1%  hours   less.     How  many   hours   did  he  work  on 
Tuesday? 

8.  A  woman  bought  12%  pounds  of  meat,  8%  pounds 
being  beef  and  the  rest  mutton.     How  many  pounds 
of  mutton  were  there? 

9.  A    girl    earned    $11X    a  week.     What    did    she 
spend  if  her  savings  were  $3%? 

10.  In  a  row  20  feet  long,  the  distance  between 
the  end  plants  is  18^  feet.     How  many  feet  are  there 
between  each  end  plant  and  the  end  of  the  row  if  the 
two  distances  are  equal? 

SUBTRACTING  COMPOUND   NUMBERS 
WRITTEN  EXERCISES 

1.  A  fanner  has  32  bushels,  3  pecks,  7  quarts  of 
seed.  He  requires  36  bushels,  1  peck,  4  quarts.  How 
much  is  he  short? 


NUMBERS  AND  PROCESSES  227 


METHOD 

32  bu.  2  pk.  7  qt.  The  question  is  to  find  the 

quantity    by    which    32    bu. 

36  bu.  1  pk.  4  qt.         2  Pk-  ?  qt-  must  be  increased 

to  make  37  bu.  1  pk.  4  qt. 

Write  these  quantities  as  shown  above.  Under 
7  qt.  write  the  number  of  quarts,  which  added  to 
7  qt.  will  make  12  qt.  (1  pk.  +  4  qt.)  Carry 
1  pk.  to  2  pk.,  making  3  pk.  In  this  column 
write  the  number  of  pecks  which  added  to  3  pk. 
will  make  5  pk.  (1  bu.  -f-  1  pk.).  Carry  1  bu.  to 
32  bu.  In  this  column  write  the  number  of  bushels 
which  added  to  33  bu.  will  make  36  bu.  Cover 
the  last  line  with  a  piece  of  paper.  On  this  write 
the  sum  of  the  two  addends,  adding  upwards. 
Compare  this  result  with  the  original  sum,  36  bu., 
etc. 


In   the  following   examples   use   the   same  method 
without  changing  the  arrangement  of  the  quantities. 

2.   Subtract.     Write  answers  directly  from  the  text 
book. 

a  £40      3s.     6d.  b   63  yd.     1  ft.     2  in. 

-£19     16s.    IQd.  -  48  yd.     2  ft.     8  in. 

c   93  gal.     2qt.  d  74  bu.     2  pk.     3  qt. 

-  44  gal.     3  qt.     1  pt.  -  28  bu.     2  pk.     6  qt. 

SIGHT  EXERCISES 

1.    (a)  From  9  Ib.  take  3  Ib.  9  oz.     (b)  From  8  bu. 
2  pk.  take  5  bu.  3  pk. 


228         WALSH'S  BUSINESS  ARITHMETIC 


METHOD 

(a)  Think  6  Ib.  (9  Ib.  -  3  lb.),  5  Ib.  7  oz.  (de- 
ducting 9  oz.).     5  lb.  7  oz.     Ans. 

(6)  Think  3  bu.  2  pk.  (8  bu.  2  pk.  -  5  bu.),  2  bu. 
3  pk.  (deducting  3  pk.)     2  bu.  3  pk.     Ans. 


2.   Give  answers: 

a  £18     6s.  b   9s.     6d.  c   4  lb. 

-  £13     10s.  -  5s.     9d.  -  1  lb.     7  oz. 

d  25  bu.     1  pk.  e   5  pk.     2  qt.  /   8  gal.     1  qt. 

-    8  bu.     3  pk.  -  1  pk.     7  qt.  -  2  gal      3  qt. 

TIME  BETWEEN  DATES 
PREPARATORY  EXERCISES 

1.  If  a  man  begins  work  at  the  opening  hour  of  May 
5,  and  finishes  at  the  closing  hour  (a)  of  May  6,  (b) 
of  May  21,  how  many  days  has  he  worked? 

2.  An  importer  receives  some  bales  numbered  con- 
secutively from  52  to  73.     How  many  bales  are  there? 

3.  How  many  fence  posts  8  feet  apart  will  be  needed 
for  a   strip   of  fence    (a)  8   feet  long?     (b)  16   feet? 
(c)  80  feet?     (d)  160  feet? 

4.  If  there  are  21  fence  posts  8  feet  apart,  what  is 
the  distance  between  the  first  and  the  last? 

The  difference  between  two  dates,  say  March  1  and 
March  31,  is  31  days  if  both  days  are  included,  29  days  if 
both  days  are  excluded,  and  30  days  if  one  is  included  and 
the  other  is  excluded. 

When  both  days  are  included,  the  time  is  stated  as  March 
1  to  March  31,  inclusive;  when  both  days  are  excluded,  it 
is  stated  as  March  1  to  March  31,  exclusive;  when  one  is 


NUMBERS  AND  PROCESSES  229 

included  and  the  other  is  excluded,  the  time  is  stated  merely 
as  March  1  to  March  31. 

In  some  places,  however,  interest  for  2  days  is  charged 
on  money  borrowed  on  March  1,  and  repaid  on  March  2, 
both  days  being  included.  Ascertain  the  practice  prevalent 
in  your  locality.  In  the  following  examples,  include  only 
1  day. 

Time  less  than  a  Year 

When  dates  are  less  than  a  year  apart,  the  time  between 
them  is  usually  found  in  days. 

WRITTEN   EXERCISES 

1.  How  many  days'  interest  is  due  on  a  loan  made 
Jul.  3,  1919,  and  paid  May  16,  1920? 


METHOD 

Jul.  28  days  Write  the  time  remaining  in 
Aug.  31  "  July  by  deducting  3  days  from  31 
Sep.  30  "  days,  thus  excluding  July  3. 
Oct.  31  "  Write  the  number  of  days  in  each 
Nov.  30  "  of  the  other  months  to  April, 
Dec.  31  "  inclusive,  remembering  that  1920 
Jan.  31  "  is  a  leap  year.  For  May,  write 
Feb.  29  "  the  number  of  days  expressed  by 
Mar.  31  "  the  date,  thereby  including  May 
Apr.  30  "  16. 

May     16  A    method    of    checking    is    to 

Total  318  days  take  the  time  as  10  months  13 
days,  which  would  make  313 
days  if  each  month  had  30  days.  Adding  6  extra 
days  for  July,  August,  October,  December,  January, 
and  March,  and  deducting  1  for  February  makes 
5  days  more  than  313. 


230         WALSH'S  BUSINESS  ARITHMETIC 

2.   Find  the  time  between: 

a  Dec.  28,  1919  and  Jan.    16,  1920 

b  Mar.  19,  1920  "  Feb.  29,  1920 

c  Jan.   22,  1919  "  May  12,  1919 

d  Aug.  17,  1918  "  Jun.   12,  1919 

e  Jan.   31,  1919  "  Aug.  24,  1919 

/  May  29,  1918  "  Mar.  22,  1919 

g  Feb.  23,  1920  "  Jun.   18,  1920 

h  Jul.    25,  1919  "  Apr.  20,  1920 

i  Sep.   27,  1918  "  Jul.    15,  1919 

j  Apr.  30,  1919  "  Sep.   21,  1919 

Bankers  use  a  table  to  ascertain  the  time  between 
two  dates. 

WRITTEN  EXERCISES 

1.  Find  the  time  that  has  elapsed  between  May  15, 
1917,  the  date  on  which  a  note  was  drawn,  and  Jan. 
3,  1920,  the  date  on  which  it  was  paid. 

In  this  case,  also,  the  practice  varies.  Some  states  require  that  first 
the  whole  number  of  years  be  taken  (2  years  from  May  15,  1917,  to  May  15, 
1919);  then  the  whole  number  of  months  (8  months  from  May  15,  1919,  to 
Dec.  15,  1919);  finally,  the  number  of  days  from  Dec.  15,  1919,  to  Jan.  3, 
1920,  viz.  19  days.  The  more  common  practice  is  the  one  given  below, 
which  assumes  that  each  month  contains  30  days. 


PROCESS 

1920  -  1  -  3  Write  1920,  first  month,  third 

1917  —  5  —  15  day,  as  the  minuend;  and  1917, 
fifth  month,  fifteenth  day,  as  the 
subtrahend.  Find  the  difference  by  the  method 
given  for  subtracting  compound  numbers  (com- 
pound subtraction). 


NUMBERS  AND   PROCESSES  231 

2.   Find  the  difference  in  time  between 

a  Apr.  17,  1916  and  Sep.   10,  1919 

b  Sep.   30,  1917  "  Jul.    12,  1920 

c  Jul.    28,  1914  "  Apr.  15,  1918 

d  Nov.  19,  1916  "  Jun.   11,  1919 

e  Feb.  17,  1915  "  Aug.  15,  1920 

/  May  22,  1918  "  Mar.  20,  1921 

g  Jan.    16,  1919  "  May  12,  1922 

h  Oct.   20,  1916  "  Feb.  18,  1920 

i  Aug.  25,  1918  "  Mar.  22,  1921 

j  Jun.    18,  1919  "  Jan.    13,  1922 

SIGHT  EXERCISES 

Find  the  number  of  days  that  elapsed  between  the 
planting  and  the  first  picking  of  the  following: 

a  Beans,  planted  May  12,  first  picking  Aug.  10 

b  Beets  "  Apr.  15,  "  "  Jun.  15 

•c  Corn  May  5,  "  "  Aug.  1 

d  Melons  "  May  15,  "  "  Aug.  20 

e  Peas  "  Apr.  5,  "  "  Jun.  10 

/  Tomato,  "  May  1,  "  "  Aug.  1 

g  Squash,  "  May  25,  "  "  Sep.   1 

h  Radish  "  Apr.  1,  "  "  May  10 

i   Onion,  "  Apr.  10,  "  "  Aug.  15 

j   Leek,  "  Apr.  15,  "  "  Aug.  15 


CHAPTER  SEVEN 

SPECIAL  TESTS 

AVOIDING  MISTAKES 

Legible  Figures 

"Blind"  figures  are  one  source  of  error.  Learn 
to  make  figures  that  are  easily  read,  and  to  write 
each  figure  in  its  proper  place. 

Do  not  make  a  correction  by  writing  a  second 
figure  on  top  of  the  first  one.  Draw  your  pen  through 
the  original  figure,  write  the  correct  one,  and  assume 
the  responsibility  for  the  change  by  affixing  your 
initials. 

Do  not  erase  anything  in  a  business  document. 
Erasures  beget  suspicion  at  times.  Make  a  necessary 
change  in  the  manner  suggested  above. 

TESTING  A  RESULT 

In  testing  any  result,  look  first  at  its  reasonableness. 
The  product  of  37  by  27  should  be  less  than  1200 
(40  X  30).  It  should  be  more  than  925  (37  X  25). 

Count  the  number  of  figures  in  a  result.  The 
product  of  2  X  4  contains  1  figure,  that  of  4  X  3 
contains  2;  the  product  of  23  X  30  contains  3  figures, 
that  of  40  X  25  contains  4,  etc.,  —  the  number  of 
figures  in  a  product  of  two  factors  being  equal  to  the 
total  number  of  figures  in  the  two  factors  or  1  less. 
In  the  latter  case  examine  the  product. 

99* 


NUMBERS  AND  PROCESSES  233 

A  pupil  in  multiplying  316  by  307  might,  by  mistake, 

place  the  first  figure  of  the  second  partial  product  in 

the  tens'  place  instead  of  in  the  hun- 

Error         dreds',    obtaining    the    incorrect    result 

316         11,692.     When  he  finds 
X  307         that    this   product   has         Correct 
^ve   figures>   °ne  fewer  316 

than   the  total    of    the         x  307 
two  factors,  he  should 
observe  that  a  5-figure 


product  must  be  greater        „„ 
than  90,000. 

Of  course,  if  he  makes  the  test  by  using  316  as  the 
multiplier,  he  will  discover  his  mistake.  This  will 
not  be  the  case  if  he  applies  the  test  of  "casting  out 
9's." 

In  testing  the  product  of  43  X  67,  of  274  X  689,  or 
of  any  other  two  factors  containing  the  same  number 
of  figures,  obtain  a  second  product  by  reversing  the 
factors. 

43  67  274  689 

X  67       X  43  X  689       X  274 

When  you  obtain  the  product  of  72  X  28769  by 
multiplying  by  72,  test  it  by  using  8  and  9,  the  factors 
of  72. 

28769  (a)    28769  X  72 

72  (6)  258,921       "  9  times  (a) 

57538          2,071,368     8  "   (6) 
201383 

2071368 


234          WALSH'S  BUSINESS  ARITHMETIC 

If  you  obtain  the  product  originally  by  using  9 
and  8  as  the  factors,  find  the  second  product  by  chang- 
ing the  order  to  8  and  9. 

The  product  of  73  X  34568,  when  first  obtained  by 
the  method  shown  at  the  left,  is  tested  by  the  one 
shown  at  the  right. 

(a)       34,568  X  73  (c)       34,568  x  73 

(6)      103,704    3  times  (a)  (d)     276,544  8  times  (c) 

2,523,464  70  times  (a)  +  (6)       2,523,464  9  times  (d)  +  (c) 

Explanations  of  these  abbreviated  processes  will 
be  given  later. 

"CASTING  OUT  9's" 

It  has  been  seen  that  a  number  is  divisible  by  9 
if  the  sum  of  the  digits  is  divisible  by  9.  By  the 
"excess"  of  9's  in  a  number  is  meant  the  remainder 
left  when  a  number  is  divided  by  9.  To  obtain  this 
excess,  find  the  sum  of  the  digits  in  the  number,  and 
divide  this  total  by  9. 

The  "excess"  of  9's  in  3460875,  for  instance,  is 
the  remainder  left  when  3  +  4  +  6  +  8  +  7  +  5,  or  33, 
is  divided  by  9;  namely,  6.  It  is  not  even  necessary 
to  divide  33  by  9  to  obtain  this  remainder,  the  "excess" 
of  33  being  3+3. 

In  practice  reject  9  when  the  sum  of  two  or  more 
digits  is  9  or  more. 

Think  7  (3+4),  13  (adding  6),  4  (rejecting  9), 
12  (adding  8),  3  (rejecting  9),  10  (adding  7),  1  (reject- 
ing 9),  6  (adding  5). 

This  process  of  finding  the  excess  of  9's  in  a  number 
is  called  "Casting  out  9V 


NUMBERS  AND  PROCESSES  235 

TESTING  A   SUM 

A  sum  may  be  tested  by  comparing  its  excess  with 

the  sum  of  the  excesses  of  the  ad- 

3461  (Exc.)  5      dends.     In    the   given    example    the 

822        "     3     excesses   of    the    addends    are   5,   3, 

1753        "     7     anc}  7j  the  sum  of  which  is  15,  of 

6036  (Exc.)  6     which  the  excess  is  6.     The  excess  of 

6036  is  6. 

That  is,  the  excess  in  a  sum  equals  the  excess  of  the 
total  of  the  excesses  of  the  addends. 

SUBTRACTION  TEST 

A    difference    may    be    similarly   tested.     In    this 
example,    the    excess    of    9's    in    the  ,        , 

•  i     •  •         •  i  iti  i       >•/          o4OJ.     (li<XC.)    O 

minuend  is  5,  in  the  subtrahend,  7. 


Since  7  is  greater  than  5,  the  latter      1793  (Exc  )  7 
is  increased  by  9,  making  this  excess 
14.     Deducting  7  gives  an  excess  of  7.     This  excess 
equals  the  one  in  the  remainder,  which  is  7. 

Another  way  is  to  add  the  excess  in  the  remainder 
to  that  in  the  subtrahend  (7+  7),  which  gives  5  as 
the  excess  in  the  minuend  (14-9). 

That  is,  the  excess  in  a  minuend  equals  the  excess  of  the 
total  of  the  excesses  of  the  remainder  and  the  subtrahend. 

The  fact  that  the  excess  of  the  total  of  the  excesses 
of  the  addends  does  not  equal  the  excess  of  the  sum, 
shows  that  the  result  is  in- 

correct;   but  the  converse 

T-    .  3461  (Exc.)  5 

is    not    true.     If    in    per-  «     3  (Exc.  6) 


forming  the  addition,  the  1753  "  7 
person  wrote  1  in  the  second  6216  (Exc.)  6 
column,  and  carried  3,  in- 


236         WALSH'S  BUSINESS  ARITHMETIC 

stead  of  writing  3  and  carrying  1,  the  excess  of  the 
erroneous  result  would  still  be  6.  The  substitution  of 
31  for  13  (or  any  other  such  transposition)  does  not 
change  the  excess,  the  total  of  the  digits  being  the 
same  in  31  as  in  13. 


TESTING  PRODUCTS 

Applying  this  test  to  products  heretofore  found, 
we  find  that  the  excess  in  2,071,368  equals  the  product 
of  the  excesses  in  28,769  and  72. 

28,769  X  72  =  2,071,368 

(Exc.)  5  X  (Exc.)  0  =  (Exc.)  0 

and  the  excess  in  2,523,464  equals  the  product  of  the 
excesses  in  34,568  and  73 

34,568  X  73  =  2,523,464 

(Exc.)  8  X  (Exc.)  1  =  (Exc.)  8 

316  X  307  =       97,012 

(Exc.)  1  X  (Exc.)  1  =  (Exc.)  1 

That  is,  the  excess  in  a  product  is  equal  to  the  excess 
of  the  product  of  the  excesses  of  the  two  factors. 

When  the  excess  of  the  product  is  not  equal  to  the 
product  of  the  excesses  there  is  a  mistake;  but  they 
may  be  equal,  and  the  product  may  still  be  wrong. 

Thus  the  erroneous  calculation  given  before 

316  X          307  =  11,692 

(Exc.)  1  X  (Exc.)  1  =  (Exc.)  1 

gives  1  as  the  excess  of  the  product  and  1  as  the  product 
of  the  factor  excesses. 


NUMBERS  AND  PROCESSES  237 

WHEN  THIS  TEST  FAILS 

The  test  by  casting  out  9's  does  not  detect  an  error 
made  by  the  transposition  of  figures,  the  total  of  the 
digits  not  being  affected  by  the  change.  It  does  not 
discover,  in  a  multiplication  example,  the  substi- 
tution of  948  tens  for  948  hundreds,  since  here  the  sum 
of  the  digits  is  also  unchanged,  their  place  value  not 
being  taken  into  consideration. 

A  BETTER  TEST—  "  CASTING   OUT   ll'S  » 
A  number  is  divisible  by  11  when  the  sum  of  the 
odd-numbered  digits  is  equal  to  the  sum  of  the  even- 
numbered  ones. 

Thus  in  253  (which  is  11  X  23),  3+2=5;  in  2574, 
(which  is  11  X  234),  4  +  5  =  7  +  2. 

The  excess  of  ll's  in  254  is  (4  +  2)  -  5,  which  is  1. 
The  excess  of  ll's  in  2576  is  (6  +  5)  -  (7+2).  To 
find  the  excess  in  this  way  begin  with  the  ones'  figure, 
and  take  from  the  sum  of  the  first,  third,  etc.,  the  sum 
of  the  second,  fourth,  etc.  The  excess  in  2,071,368  = 
(8  +  3  +  7  +  2)  -  (6  +  1  +  0)  =  20  -  7  =  13,  the  ex- 
cess of  which  is  2.  This  agrees  with  the  remainder 
obtained  by  dividing  this  number  by  11. 

11)2071368 

188306  Rem.  2 

In  practice,  however,  find  the  excess  of  ll's  by 
continued  subtraction  beginning  at  the  left. 

To  find  the  excess  of  ll's  in  2,071,368,  take  2  from 
0,  the  remainder  from  7,  the  remainder  from  1,  the 
remainder  from  3,  the  remainder  from  6,  the  remainder 


238         WALSH'S  BUSINESS  ARITHMETIC 

from  8,  increasing  each  minuend  by  11  when  it  is  less 
than  the  corresponding  subtrahend.  The  successive 
results  are  9  (2  from  0+  11),  9  (9  from  7+  11),  3 
(9  from  1  -f  11),  0  (3  from  3),  6  (0  from  6),  2  (6  from 
8),  the  last  remainder,  2,  being  the  excess. 

TESTING  BY  EXCESS   OF  ll'S 
The  following  is  the  test  of  the  correct  addition 

3461  (Exc )  7  1  reSUlt  giV6n  °n  a  previous 

822         "     8     (Exc.  8)      page*       The   incorrect    an~ 

1753        "     4  1  swer,    6216,    which   is   not 

6036  (Exc.)  8  detected  by  the  excess  of 

9's,  gives   1   as  the  excess 

of  ll's,  which  disagrees  with  8,  the  excess  of  the  total 
of  the  addends'  excesses. 

Testing  the  two  products  found  in  multiplying  316 
by  307,  the  following  are  the  results  by  casting  out 
ll's: 

316  X  307  =     97,012 

(Exc.)  8  X  (Exc.)  10  =  (Exc.)  3 

In  this  the  excess  of  80,  the  product  of  8  X  10,  the 
excesses  of  the  factors,  is  3,  which  agrees  with  the 
excess  of  97,012  in  the  above  answer. 

The  excess  of  ll's  in  the  wrong  answer  (11,692),  is 
10,  which  shows  that  a  mistake  has  been  made  some- 
where. 

SELECTING  THE   SAFER  TEST 

The  fact  that  it  is  slightly  easier  to  apply  the  test 
of  casting  out  9's  than  that  of  casting  out  ll's  is  no 
reason  for  the  employment  of  the  one  that  is  less  cer- 
tain. 


NUMBERS  AND  PROCESSES  239 

TESTS   OF   SUMS  AND   DIFFERENCES 

Inasmuch  as  it  probably  takes  longer  to  apply 
"excess"  tests  in  addition  and  in  subtraction,  check 
these  operations  by  the  method  suggested  for  each, 
testing  a  sum  by  adding  "down"  when  the  first  result 
is  obtained  by  adding  "up," — and  testing  a  remainder 
by  combining  it  with  the  subtrahend  to  make  the 

minuend. 

TESTING    QUOTIENTS 

When  the  division  is  exact,  the  dividend  is  equal  to 

72)2  071  368         the  product  of  the  <luotient  by  the 
divisor.     In  testing  the  result,  apply 

the  method  shown  in  the  multiplica- 
tion example  previously  given. 

When  there  is  a  remainder,  add     31)1896 
the  excess  of  the  remainder  to  the  90  Rem-  6 

product  of  the  excesses  of  the  quotient  and  the  divisor. 

Quotient  90       (Exc.)        2 

Divisor     21       (Exc.)  X  10 

Product  of  excesses  =  20  the  excess  of  which  is  9 
Remainder  +_6     "       "      "       "      "6 

Total  26     "       "      "       "      "  4 

The  excess  of  1896,  the  dividend,  is  also  4 

DECIMAL  RESULTS 

In  testing  a  result  by  casting  out  ll's,  consider 
every  figure  that  enters  into  it. 

The  cost  of  14  yards  at  $1.125  per  yard  is  given  as 
$15.75.  If  the  ll's  are  cast  out  of  8 

this  product,  the  excess  is  round  to  -^  (Exc  )  3 

be  2,  which  does  not  agree  with  the    $15  750  (Exc  )  9 
product  (9)  of  the  factor  excesses. 


240          WALSH'S  BUSINESS  ARITHMETIC 

By  taking  the  result  obtained  by  the  multiplication, 
15.750,  thus  including  the  rejected  decimal  cipher,  the 
excess  is  9. 

In  testing  a  quotient,  include  as  a  part  of  the  divi- 
.  dend  any  decimal  ciphers  that  need  to 

be  annexed  (even  when  not  written)  to 
$1.125  T        Al 

produce  the  quotient. 

When  a  number  contains  two  or  1.625  (Exc.)  8 

more  terminal  decimal  ciphers,  re-  X  48  (Exc.)  4 

ject  them  by  twos.     The  excess  in  78-000  (Exc-)  10 
78.0  is  the  same  as  in  78,000. 

SIGHT  EXERCISES 

1.  Give  the  excess  of  ll's  in  each  of  the  following 
products  when  it  contains  all  of  the  figures  of  the  re- 
sult. 

a  13764.83  b  20306.5  c  .035007 

d  20403.14  e  42631.4  /  .002464 

g  31060.25  h  56009.8  i  .437692 

2.  Give  the  excess  of  ll's  in  each  of  the  following 
products  from  which  one  (or  three)  terminal  decimal 
ciphers  has  been  dropped: 

a  3674;183  b  563.0062  c  .703005 

d  4140.002  e  431.6024  /  .040604 

g  5206.301  h  890.0056  i  .269473 

3.  Give  the  excess  of  9's  in  the  previous  sets. 


CHAFFER  EIGHT 

MULTIPLICATION 

ONE  FACTOR  AN  INTEGER 

SIGHT  DRILLS 


A 

B 

C 

D 

E 

F 

G 

H 

I 

J 

a  9 

12 

21 

35 

43 

51 

62 

72 

80 

99 

6  8 

13 

23 

34 

45 

52 

65 

74 

81 

98 

c  7 

14 

22 

33 

44 

53 

63 

75 

82 

97 

d  6 

15 

25 

32 

41 

54 

61 

73 

83 

96 

e  5       16       24       31       42       55       64       71       84       95 

1.  Multiply  by  2,  by  3,  by  4,  by  5,  by  6,  by  7, 
by  8,  by  9. 

Give  answers  rapidly  (a)  by  columns,     (b)  By  lines. 

2.  Multiply  by  15:    (a)    6,  (b)  12,  (c)  21,  (d)  22,  (e) 
44,  (/)  55 

3.  Multiply  by  21:    (a)  8,  (b)  13,  (c)  24,  (d)  32,  (e) 
41,  (/)44 

ORAL  PROBLEMS 

1.  In  a  year  of  52  weeks  how  much  does  a  person 
earn  who  receives   (a)  $6  a  week?     (6)  $7?     (c)  $8? 
(d)  $9?     (e)  $12?     (/)$15?     (0)  $18?     (h)  $25? 

2.  How  much  less  than  $1000  a  year  is  the  income 
of  a  girl  earning  $18  a  week? 

3.  What  is  the  weight  (a)  of  120  bushels  of  potatoes 
at  60  pounds  to  the  bushel?     (b)  Of  80  bushels  of  oats 
at  32  pounds  to  the  bushel? 

241 


242          WALSH'S  BUSINESS  ARITHMETIC 

4.  How  many  yards  are  there  in  12  pieces  of  lining 
averaging  45  yards  to  the  piece? 

5.  How  many   ounces   are  there  in   11   pounds  4 
ounces? 

6.  Find  the  cost  (a)  of  84  yards  of  dress  goods  at 
25  cents  a  yard.     (6)  Of  25  yards  of  silk  at  88  cents  a 
yard. 

7.  The  sales  of  a  small  store  average  $35  for  the  six 
days  of  a  week.     If  the  sales  for  five  days  average  $30, 
what  is  the  amount  of  Saturday's  sales? 

8.  What  is  the  freight  on  16  tons  at  $2%  a  ton? 

9.  How  many  square  rods  are  there  in  a  rectangular 
field  21  rods  long  and  16  rods  wide? 

10.  Find  the  volume  of  a  rectangular  block  of  marble 
whose  dimensions  are  2%  ft.,  by  4  ft.,  by  3%  ft. 

SIGNS   OF  MULTIPLICATION 

To  indicate  that  one  number  is  to  be  multiplied  by 
another,  a  cross  (x)  is  placed  between  them. 

The  expression  3  X  5  is  read  "3  times  5,"  or  "3 
multiplied  by  5." 

To  indicate  that  3^  is  to  be  multiplied  by  5,  the 
expression  may  be  written  3^  X  5,  or  5  X  3^.  In  this 
second  form  it  is  read  "5  times  3?f,"  in  order  to  an- 
nounce the  abstract  number  as  the  multiplier.  How- 
ever, in  finding  the  weight  of  275  pack-  5  „ 
ages  of  sugar  each  containing  5  pounds,  ^^ 

multiply  275  by  5,  even  if  you  arrange     — 

the  factors  in  the  manner  shown  herewith. 

Another  way  to  indicate  multiplication  is  to  use  a 
period  between  the  factors,  writing  it  above  the  line, 


NUMBERS  AND   PROCESSES  243 

9-15-17.  The  period  is  employed  in  algebraic  work  to 
avoid  the  use  of  a  sign  that  might  be  mistaken  for  the 
letter  x.  . 

In  the  European  countries  that  use  a  comma  to  denote  a  decimal  point, 
the  period  employed  as  a  sign  of  multiplication  is  written  on  the  line. 

The  product  of  two  literal  numbers  is  indicated  in 
algebra  by  writing  the  letters  together,  without  an 
intervening  sign.  Thus  ab  means  a  times  b  (or  b  times 
a).  To  indicate  the  product  of  2  times  the  sum  of  x 
and  4,  the  expression  takes  this  form,  2  (a: +  4),  no 
multiplication  sign  being  employed. 

The  expression  16'  X  3'  X  8",  used  by  mechanics  in 
denoting  dimensions  is  read  "18  feet  by  3  feet  by  8 

inches." 

WRITTEN  EXERCISES 

1.  (a)  At  $1.23  a  yard,  find  the  cost  of  16  yards  of 
silk,  (b)  Find  the  cost  of  123  yards  of  muslin  at  16 
cents  a  yard. 


METHOD 

(a)  Since  the  figures  of  the  multiplicand  are  small, 
write  the  answer  directly  from  the  book. 

(b)  Use  16  as  the  multiplier. 

TEST 

First  write  the  product  of  $1.23  by  4;   then  mul- 
tiply this  product  by  4. 


The  multiplicand  and  the  multiplier  are  called  the  FACTORS 
of  a  product. 

To    obtain    a   product,    use    either    factor    as    the 
multiplier. 


244         WALSH'S  BUSINESS  ARITHMETIC 
2.   Write  answers  directly  from  the  book. 

a  16  X  142  b  311  X  18  c  16  x  420  d  322  X  23 
e  21  X  231  /  212  X  14  g  18  X  333  h>  221  x  41 
i  32  X  412  j  612  X  24  A:  24  X  444  /  202  x  36 

Test  products  by  writing  on  a  second  strip  the  suc- 
cessive products  obtained  by  using  the  factors  of  the 
multiplier. 

MULTIPLYING  AND  ADDING 
ORAL  PROBLEMS 

1.  How  many  quarters  are  there  in  21%? 

2.  What  is  the  cost  of  five  pounds  of  8-cent  sugar 
and  25  cents'  worth  of  eggs? 

3.  How  many  inches  are  there  in  10  feet  11  inches? 

4.  Change  9%  to  an  improper  fraction. 

Each  of  the  foregoing  requires  the  finding  of  a  prod- 
uct and  the  combination  of  the  latter  with  a  given 
number. 

SIGHT  EXERCISES 

1.  A  farmer  paid  a  debt  by  giving  12  tons  of  hay 
at  $15  a  ton  and  $20  in  cash;  how  much  did  he  owe? 

2.  Give  the  value  of  the  following: 

a    16  •  25  +  59     b    34  +  (6  x  50)     c  83    +  12  X  33% 

d  (9  x  12)  +  20     e   (9  X  12)  +20      /  12%  X  48  +  67 

Remember  that  the  product  of  the  numbers  connected 
by  a  sign  of  multiplication  is  to  be  added  to  the  remaining 
number. 

In  a,  add  59  to  the  product  of  16  by  25;  in  c  add  83  to 
the  product  of  12  times  33%,  combining  the  numbers  con- 
nected by  a  sign  of  multiplication  before  performing  the 
indicated  addition. 


NUMBERS  AND  PROCESSES  245 

In  6  and  in  e  the  parenthesis  is  unnecessary,  but  its  use 
serves  to  indicate  to  a  person  unaware  of  the  effect  of  the 
multiplication  sign  that  the  numbers  within  it  are  to  be  com- 
bined into  a  single  number. 

WRITTEN  EXERCISES 

1.  How  many  square  inches  are  there  in  the  surface  of 
a  steel  plate  containing  8  square  feet  96  square  inches? 


PROCESS 

8  sq.  ft.      96  sq.  in.         There  are  144  square  inches 

1248  sq.  in.      in  a  square  foot.     In  8  square 

feet    there   are   8    times   144 

square    inches.     To   the    product   add    96    square 
inches. 

Do  this  in  one  operation.    . 
Think  32  (8X4),  38  ("adding-in"  6);  write  8. 
Think  32  (8X4),  35  (carrying  3),  44  ("adding- 
in"  9);   write  4. 

Think  8  (8  X  1),  12  (carrying  4);  write  12. 

TEST 

Divide  1152  (1248  -  96)  by  8. 


2.   Find   the   value    (a)  of  (9  X  86)  +  129.     (6)  Of 

237+  (7X  97). 


PROCESS 

a  (9  X  86)  +  129  b  237  +  (7  X  97) 

Ans.     903  916    Ans. 

Write  the  result  under  the  number  to  be  "added- 


in." 


246         WALSH'S  BUSINESS  ARITHMETIC 

3.   Find  the  value  of  each  of  the  following: 

a  (4  x  38)  +95  b   77  +  (9  x  83)  c  (10  x  87)  +  261 

d  (5  x  46)  +87  e   55  +  (8  x  67)  /  (20  X  43)  +  129 

g  (6  x  54)  +  66  h  68  +  (7  x  95)  i  (30  X  52)  +  104 

j   (7  X  62)  +59  k  86  +  (6  X  79)  I  (40  X  23)  +  115 

SIGHT  EXERCISES 

1.  (a)  How  many  times  87  is  261?     (b)  How  many 
times  87  is  (10  X  87)  +  261? 

2.  How  many  times  43  is  (20  X  43)  +  129? 

3.  How  many  times  52  is  (30  X  52)  -f  104? 

4.  How  many  times  23  is  (40  X  23)  +  115? 

Business  Ways 

The  pupil  who  thinks  it  impossible  for  him  to  dis- 
pense with  any  of  the  crutches  he  learned  to  employ 
in  the  lower  grades  should  at  least  become  acquainted 
with  the  fact  that  there  are  other  and  shorter  ways 
of  performing  operations.  Even  if  he  cannot  use  all  of 
those  suggested,  he  should  occasionally  try  some  of 
them. 

The  methods  recommended  are  used  by  elementary 
pupils  somewhere.  They  do  not  include  types  of 
combinations  that  have  only  a  limited  application. 

MULTIPLIERS  OF  MORE  THAN  ONE  FIGURE 
WRITTEN  EXERCISES 

1.  How  many  square  rods  are  there  in  a  rectangular 
plot  87  rods  long  and  43  rods  wide? 


NUMBERS  AND  PROCESSES  247 

PROCESS 

One  Way 

87  (rd.)  Place    the    right-hand 

X  43  (rd.)  figure  of  the  product  by 

261  3  under  3,  of  the  product 

348  by  4  under  4.     Combine 

3741  (sq.  rd.)  Ans.      the  Partial  Products. 

Saving  a  Line 

87  (rd.) 
Write  the  product  by  3.  43     " 

Under  it  draw  a  line,  and  then         TTT 

multiply  87  by  4  (tens). 

3741  (sq.  rd.) 

Instead  of  writing  this  partial  product,  combine 
it  with  the  first  partial  product. 

First  bring  down  1,  the  one's  figure  of  the  product 
by  3. 

Think  28  (4x7),  34  (adding  6);   write  4. 

Think  32  (4X8),  35  (carrying  3),  37  ("adding 
in"  2);  write  37.  ANS.  3741  (sq.  rd.) 

TEST 

Multiply  43  by  87. 

2.   Find  products.     Test.     Try  the  short  method. 

a    94  X  86  b  73  X  57  c    63  x  84  d  78  X  74 

e    28  x  69  /  94  X  96  g    54  X  72  h  86  x  36 

i    46  x  54  j  29  x  27  A:   87  X  93  /  56  x  52 

m  68  x  83  n  48  X  43  o    65  x  26  p  39  X  79 

q    37  X  67  r  35  X  62  s    42  X  42  t  24  X  58 

u   53  X  47  v  89  X  38  w   76  x  34  a;  32  X  82 


248         WALSH'S  BUSINESS  ARITHMETIC 

3.   Find  the  cost  of  76  acres  of  land  at  $85  an  acre. 


METHOD 

$85  Many  accountants  begin  mul- 

76  tiplication    with    the    left-hand 

595  figure. 

$6460  Ans.         Write  the  first  figure  of  the 
product    by    7    under    7,    etc. 
Draw  a  line,  multiplying  by  6;  think  30    (6x5); 
write  0. 

Think  48  (6x8),  51  (carrying  3),  56  (adding  5); 
write  6.     Carry  5  to  59  and  write  64. 


4.   Multiply.     Save  a  line. 


a  27  X  34 

b  23  X  37 

c  75  X  43 

d  38  X  92 

e  53  X  96 

i  79  X  27 

/  54  X  57 
j  59  X  98 

g  45  X  49 
k  56  X  74 

h  67  X  59 
/  93  X  58 

m  64  X  63 

n  47  X  64 

o  82  X  68 

p  97  X  82 

q  38  X  59 

r  57  X  47 

s  32  X  49 

t  93  X  84 

u   28  X  63         v   72  X  74         w  67  X  46         a:  59  X  45 
Omit  as  many  figures  as  you  can. 

aa     28  X  35  X  73  bb   24  X  38  X  64  cc  76  X  45  X 

dd     54  X  97  X  29  ee    55  X  58  X  76  //  57  X  73  X 

gg     78  X  26  X  64  hh   97  X  95  X  94  ii  83  X  69  X 

jj      65  X  37  X  56  kk  48  X  63  X  35  II  33  X  48  X 

mm  39  X  58  X  43  nn  58  X  46  X  73  oo  68  X  74  X 

5.  Edward  Regan  bought  127  covers  from  Mr. 
Plumridge  at  $2.85  apiece,  (a)  How  much  was  paid? 
(b)  What  would  be  the  cost  of  712  covers? 


NUMBERS  AND  PROCESSES  249 


PROCESS 


(a)  $2.85 

x  127  First  multiply  by  7,  then  by 

— — -  12   (tens);    combine  this  prod- 

uct with  the  first. 


$361.95  Ans. 

Multiply  by   12;    then  by  7   (hun-               ^ 
dreds).     Bring  down  20,  the  ones  and  - 

the  tens  of  the  product  by  12. 

$2019.20 

w 

Note  in  (6)  that  5,  the  right-hand  figure  of  the 
product  of  7  times  5,  belongs  in  the  hundreds'  place 
(under  the  7) ;  hence,  combine  it  with  4  of  the  first 
partial  product,  to  make  39;  etc. 


6.   Find    products.     Try    to    limit    the    number    of 
figures  you  use. 


a 

127 

X 

195 

6 

138 

X 

234 

c 

149 

X 

321 

d 

116 

X 

586 

e 

129 

X 

639 

f 

117 

X 

845 

9 

316 

X 

432 

h 

169 

X 

543 

i 

178 

X 

232 

j 

712 

X 

591 

k 

912 

X 

396 

I 

711 

X 

458 

m 

611 

X 

685 

n 

512 

X 

345  J 

0 

812 

X 

942 

P 

134 

X 

347 

q 

615 

X 

235 

r 

184 

X 

374 

s 

414 

X 

253 

t 

161 

X 

357 

u 

418 

X 

224 

V 

156 

X 

624 

w 

417 

X 

192 

X 

149 

X 

328 

Learn  to  multiply  numbers  below  10  by  numbers 
below  20. 

aa  128  X  196  X  163  bb  117  X  537  X  152 

cc   812  X  642  X  711  dd  314  X  628  X  143 


250          WALSH'S  BUSINESS  ARITHMETIC 

7.  A  school  used  in  a  year  134  gross  of  pens. 
(a)  How  many  pens  were  used?  (6)  How  many  pens 
are  there  in  56  gross? 


METHOD 

(a)       134  (gro.)  X  144 
1608  (12  X  134) 


19296  (pens)  (12  X  1608)  Ans. 
(b)     144  pens  X  56 
1008  (7  X  144) 


8064  pens  (8  X  1008)  Ans. 
In  (a)  use  the  factors  12  and  12;  in  (b)  use  7  and  8. 

TEST 

(a)       134  (gro.)  X  144 
2144  (16  X  134) 
X9 


19,296  (pens)  (9  X  2144) 
(b)       144  pens  X  56 
1152  (8  X  144) 
8064  pens  (7  X  1152)  Ans. 

In  (a)  use  16  and  9  as  factors;   in  (b)  reverse  the 
order  of  the  factors. 

Do    not    write    the    expressions    in    parenthesis 
(12  X  134),  (12  X  1608),  (7  X  144),  etc. 


Some  accountants  think  that  they' save  time  by  the  employment  of  the 
factors  of  the  multiplier.  These  can  frequently  be  used  to  advantage  in 
testing  a  product  obtained  in  another  way. 


NUMBERS  AND  PROCESSES  251 

8.  Find  products,  using  factors: 

a  32  X  647  b  56  x  389  c  52  X  587  d  36  x  328 
e  64  X  267  /  72  x  456  g  63  x  195  h  28  X  419 
i  96  X  853  j  78  X  323  k  54  X  635  I  42  x  926 

9.  An  agent  bought  308  horses  at  an  average  of 
$209  a  head.     How  much  did  they  cost? 


One  Way 
$209 


Place  the  right-hand  figure  of 
the  product  by  8  under  8,  of  the 
product  by  3  under  3.  Ignore 
the  cipher  in  the  multiplier. 


$64,372  Ans. 

The  Other  Way 

Bring  down  72.     Multiply  209  $209 

by  3  and  "add  in"  16,  the  remain-  308 

ing  figures  of  the  first  partial  prod-  1672 

uct-  $64,372  Ans. 

Test  by  multiplying  308  by  209. 


10.   Find  products 


a  709  X  805 

b  208  x  906 

c  307  x  709 

d  406  X  608 

e  505  X  409 

/  609  X  209 

g  708  X  507 

h  807  X  306 

i  906  x  408 

j  706  X  409 

k  607  X  407 

1  306  X  603 

m  405  X  907 

n  504  X  506 

o  704  X  407 

p  609  X  208 

q  805  X  508 

r  809  X  908 

s  906  X  305 

t  207  X  702 

u  908  X  607 

252          WALSH'S  BUSINESS  ARITHMETIC 

11.    Find  the  cost  (a)  of  213  acres  of  land  at  $164 
an  acre.     (b)  Of  321  acres  at  $416  an  acre. 


A  Short  Way 

(a)  $164         Multiply  by  3,  placing  the  right- 
X213      hand  figure  of  the  product  under  3. 

492          Obtain  the  product  by  21  (tens)  by 

3444        multiplying  492  by  7   (tens).      Why? 

$34  932      Place    the   right-hand    figure    of    this 

product  under  1. 

(b)  Multiply  by  3  (hundreds),     (b)    $416 
placing  the  right-hand  figure  of          X  321 
the    product    under  3.     Obtain          1248 
the  product  by  21  by  multiplying  8736 

1248  by  7.     Place  the  right-hand       $133)536  Ans. 
figure  of  the  product  under  1. 

A  Shorter  Way 

(a)  $164 

Bring  down  2,  then  prefix  7 

(tens)  times  492  with  49  (tens) 

added  in. 
$34,932  Ans. 

b  $416 

(b)  Combine  1248  (hundreds)       X  321 
with  7  times  1248.  1248 


"  " 


$133,536  Ans. 


12.  Find  products: 

a  122  X  189   b  123  X  279  c  153  X  355  d  246  X  497 

e  212  X  918   /  312  X  927  g  315  X  535  h  624  X  749 

i  427  X  568   j  567  X  364  k  459  X  328  /  287  X  546 

m  742  X  856   n  756  X  436  o  945  X  832  p  728  X  564 


NUMBERS  AND  PROCESSES 


253 


13.   Find  the  cost  of  3868  pounds  of  Rio  coffee  at 
12.84  cents  a  pound. 


PROCESS 


3868 
$.1284 
46416 


Exc.  7 
Exc.  8 
Exc.  1 


Exc.  1 


Write  12.84^  as 
dollars,  four  decimal 
places.  Although  it 
is  a  concrete  number, 
use  it  as  the  multi- 
plier. 

First  multiply  by  12,  placing  the  right-hand  figure 
of  the  product  under  2.  Multiply  this  product  by 
7,  placing  the  right-hand  figure  of  the  product  under 
4.  During  the  multiplication  "add  in"  46416. 

In  giving  the  answer  retain  only  the  two  decimal 
places  representing  cents. 


TEST  BY  CASTING  OUT  ll'S 

Casting  out  ll's,  the  excess  in  the  multiplicand  is  7; 
in  the  multiplier,  8;  the  product  of  these  excesses  is 
56,  of  which  the  excess  is  1.  The  excess  of  the  product, 
4966512,  is  1. 

In  finding  this  last  excess  include  12,  the  figures  can- 
celed in  giving  the  answer. 

14.   Multiply.     Test  by  reversing  the  factors. 


a  1177  X  4206 
d  3612  X  1296 


b  8407  X  1272 
e  8811  X  1248 


c  12,144  X  11,132 
/  12,132  X  11,088 


254          WALSH'S  BUSINESS  ARITHMETIC 

15.  At  an  average  of  765  pounds  to  the  acre,  what 
will  be  raised  (a)  on  18  acres?  (b)  On  81  acres?  (c)  On 
102  acres?  (d)  On  201  acres?  (c)  On  316  acres? 


PROCESS 

When  there  is  a  1  in  the  multiplier,  write  the 
latter  alongside  the  multiplicand,  and  make  it  one 
of  the  partial  products  without  writing  it  a  second 
time.  Do  this  whether  you  "add-in"  the  second 
partial  product  or  not. 

(a)  18  X  765  Ib.  (b)  81  X  765  Ib. 

13,770  Ib.  Ans.  61,965  Ib.  Ans. 

(c)  102  X  765  Ib.  (d)  201  X  765  Ib. 

78,030  Ib.  Ans.  153,765  Ib.  Ans. 

(e)  316  X  765  Ib.  In  W  use  765  for  the 

2295  first  partial  product  of 

4590  765  by  1  (ten).     Mul- 

««J40lb.  Ans.         ^fr  by  S   Hundred) 
for  the  second  partial 

product.  Multiply  this  by  2  for  the  third  partial 
product,  placing  the  right-hand  figure  in  the  ones' 
column. 


Accustom  yourself  to  begin  with  any  figure  of  the  mul- 
tiplier. There  are  advantages  at  times  in  beginning  with 
the  left-hand  figure  rather  than  with  the  ones'  figure. 

16.  Multiply: 

a  879  X  17     b  789  X  107     c  978  X  316 
d  786  X  71     e  687  X  701     /  876  X  613 


NUMBERS  AND  PROCESSES  255 

17.  What  is  the  weight  of  a  piece  of  armor  plate 
containing  374  cubic  feet,  at  the  rate  of  476  pounds 
to  the  cubic  foot? 


PROCESS 

476  Ib.  When    you    require    three 

X  374  partial  products  in  performing 

1904  a  multiplication  do  not  "add 

3332  in."     Check  the  product  by 

1428  reversing   the   factors   or   by 

Ib.  Ans.  castinS  out  u's- 


18.  Multiply.  Test  by  casting  out  ll's: 

a  379  X  286  b  973  X  421  c  845  X  754  d  417  X  278 

e  536  X  768  /  784  X  230  g  903  X  518  h  623  X  319 

i  473  X  926  j  245  X  397  k  724  X  839  I  956  X  680 

m  638  X  817  n  413  X  947  o  365  X  365  p  429  X  398 

q  219  X  609  r  937  X  346  s  158  X  415  t  538  X  709 

u  498  X  794  v  734  X  457  w  673  X  295  x  462  X  897 

ONE  FRACTIONAL  FACTOR 
DRILL  EXERCISES 

1.   Give  answers: 


a    %of84 

6  96  x  % 

c    YQ 

of  54 

d  78  xYz 

e    %  "  48 

/   64  x% 

g  % 

"36 

h  84  X  K2 

i    %   "84 

j    48  X  % 

k  % 

"72 

I    60  X  % 

w  %   "48 

n  56  X  7/s 

o   % 

"  81 

p  96  X  Ke 

g   X  "84 

r   96  X  Yi2 

s    % 

"45 

/    80  X  %5 

tt  X  "  96  »  48  x  &  w  %   "  63  x  64  X 


256         WALSH'S  BUSINESS  ARITHMETIC 

2.   Multiply: 

a    M  of  83             b  97  X  X              c     %  of  13  d  15  X  % 

e    X  "  21             /  33  x  X             0    %   "  U  h  11  X  % 

i    %  "  95             j  17  x  X              fc  X      "  82  Z    85  X  X6 

m  X  "  U              n  13  X  %              o    %    "  43  p  27  x  Ke 

q    %  "  88             r  95  X  /i2             *    X     "   16  <   15  X  KG 

w    %  "  35             v  13  X  ^12             w  X    "  17  x  13  X  KG 

SIGHT  EXERCISES 

1.   What  is  the  cost  of  (a)  12  pounds  of  sugar  at 
(6)  Of  4%  pounds  of  meat  at  32j 


PROCESS 

(a)  Think  S  (tf  of  12),  9  (3  times  3).     Think  84  (7 
times  12),  93  (carrying  9).    Write  93.     93^  Ans. 

(b)  Think  128  (4  X  32),  144  (carrying  16,  %  of  32). 
Write  144.     $1.44  Ans. 


2.  Give  products: 

a  66  X  VA  b  1/2  X  52  c  63  X  l)i 

d  84  X  IX  «  IK  X  84  /   66  X  1% 

g  56  X  IX  /i  IX  X  60  i   84  X  IX 

j  20  X  1%  k  IX  X  88  Z    81  X  IX 

m  24  X  1%  n  1%  X  81  o  36  x  1% 

p  48  X  IX  q  1%  X  45  r   54  X  \% 

s  32  X  1%  t  \%  X  56  w  40  X  1% 

tr  16  X  IX  w  1%  X  27  x  60  X  1% 

3.  Multiply: 

a  20  X  IX  b  14  X  2/2  c  15  X  2X 

d  17  x  IX  «  15  X  3^  /  16  x  3/3 

9  19  X  IX  *  16  X  2X  i  17  X  2X 

j  22  X  IX  &  30  X  3X  *  21  X  3% 


NUMBERS  AND  PROCESSES  257 

m  23  X  1%  n   18  x  2%  o  13  X  2% 

p    37  x  IKo  ?    16  X  3%  r    17  X  3% 

5    25  X  1&  <    27  X  2%  u  28  X  2% 

0    33  X  IMe  to  20  X  4Xo  x  21  X  4Mo 

WRITTEN  EXERCISES 

1.   How  many  pounds  of  flour  are  there  in  18  bags 
containing  24%  pounds  each? 


PROCESS 

Think  9  (18  halves). 

Think  72  (18  times  4),  81  (carrying  9);  write  1. 

Think  36  (18  times  2),  44  (carrying  8);  write  44. 

441  Ib.  Ans. 

Test  by  using  2  and  9  as  factors. 


NOTE:  By  taking  2  as  the  first  factor,  the  first  product  is  an  integer. 

2.  Write  answers  from  the  book.     Test: 

a  12X110%    6  110)4X24     c  8  X  112%    d  231%  X  15 
e  10  X  346%    /  108K  X  20     g  6  X  109%     h  322%  X  18 

3.  Mr.  Schlaefer  raised  an  average  of  112%  bushels 
of  potatoes  to  the  acre.     What  was  the  yield  of  a  24- 
acre  field  at  that  rate? 


PROCESS 


112%  bu.  Think  18  (%  of  24) 

X  24  Think  48  (24  X  2),  66  (carrying 

2706  bu.  Ans.  18).    Write  6. 

Think  24  (24  X  1),  30  (carrying  6);  write  0. 
Think  24  (24  X  1),  27  (carrying  3);  write  27. 


258          WALSH'S  BUSINESS  ARITHMETIC 

4.  Write  answers  from  the  book: 

a    8  X  246%  6  246%  x  12  c  212%  X  24 

d    9  X  246%  e  325%  X  12  /  111%  X  32 

g    6  x  246%  h  418%  X  12  i  101%  x  48 

j    8  X  275%  k  522%  X  12  /  321%  X  18 

m  8  X  317%  n  607%  X  12  o  321%  X  15 

5.  How  many  yards  are  there  in  29  pieces  of  ging- 
ham averaging  35%  yards  to  the  piece? 


PROCESS 

35%  yd. 
X  29  Multiply  %  by  29,  by  multi- 

4)87~  Paying  29  by  3  and  dividing 

the  product  by  4  (do  not  write 
n%  4).     To  the  result,  21%,   add 

9  times  35,  and  2  (tens)  times 
35. 


1036%  yd.  Ans. 

29 

TEST  X  35% 

Multiply    29    by    36,       JZi_  Product  by  _6 
and   from    the    product       1044  *  36 

deduct  %  of  29.  -7/4  _% 

1036%         "         "  35% 


6.  Multiply: 

a    45%  X  79  6  74  X  73%             c  16%  X  129 

d    32%  X  83  e  53  X  81%            /  17%  X  135 

g    63%  X  67  h  65  X  64%            i  18%  X  215 

j    24%  X  55  A:  81  X  43%            I   19%  X  223 

m  58%  X  91  n  95  X  52%            o  15%  X  329 

7.  What  is  the  cost  (a)  of  123  shares  of  stock  at 
$83%  a  share?  (6)  Of  137  shares  at  $85%  a  share? 


NUMBERS  AND  PROCESSES  259 


PROCESS 

(a)    123  ^se  ^e  Pr°d" 

$83%  uct    b^    3    as 

T>        J         4.   1          O  tne       firSt       Par~ 

369  Product  by  3  . .  , 

„       (f  tial      product. 

984~'  "       "    s'ftens)  Divide  this  by 

4  for  the  prod- 


$10301%  Ans.  uct  by  % 

First    multiply    137  $855/ 

by  5,  then  by  %  by  — - 

j'  *j-  4.1,      ^  695    Product  by  5 

dividing       the    first  „         / 

oD  « 


$11741%  Ans. 


8.  Multiply: 

a  13%  x  25  b  126  x  15%  c  237  X  23% 

d  27%  x  37  e  217  X  37%  /  369  X  42% 

9.  Multiply  267  (a)  by  %.     (b)  By  9%.     (c)  By  19%, 
(d)  By  39%.     (e)  By  49%. 


PROCESS 

(a)    267X%  (b)      267  X  9% 

Less  %  33%  2670  Product  by  10 

Ans.    233%  Less       53%       "        "     % 

2616%  Ans. 

(c)     267  X  19%  (d)     267  X  39% 

5340  Product  by  20  10680  Product  by  40 

Less_89          "       "    %  66%       "        "     % 

5251  Ans.  10613%  Ans. 


260          WALSH'S  BUSINESS  ARITHMETIC 
10.   Find  products: 


a  %X365 

6  %X291 

c  9%  X  58 

d  19%  X  98 

e  %X213 

/  %X577 

9  9%  X  63 

h  29%  x  83 

i  %  X  415 

j  %  X  364 

k  9%  x  95 

/  39%x71 

m  %  X  127 

n  %  X  427 

o  9%  x  89 

p  49%  X  65 

g  %o  X  567 

r  %  X  336 

s  9%  X  77 

t  59%  X  77 

w  %  X  643 

v  %  X  616 

w>  9%  X  97 

x  69%  X  83 

MULTIPLYING    FRACTIONS 
GENERAL  METHOD 

WRITTEN  EXERCISES 

1.  How  many  square  yards  of  oil  cloth  are  there 
in  a  piece  57%  yards  long  and  (a)  2%  yards  wide? 
(fr)  3%6  yards  wide? 


PROCESS 
43        7 


gf  QQI 

(a)  57^  X  n  =  ^  X  -  -=  150}^  (sq.  yd.)  Ans. 

p          2 


Omit  the  denomination.  Change  each  mixed 
number  to  an  improper  fraction.  Cancel.  Write 
the  product  of  the  new  numerators  over  the  new 
denominator.  Reduce  to  a  mixed  number.  After 
the  result  write  sq.  yd.  in  a  parenthesis. 

Use  no  figures  beyond  those  shown  above. 

(6)  57XXSXe=  -   -X"  =  ? 

o  ID 


NUMBERS  AND  PROCESSES  261 

2.   Find  products: 

a  44%  X  9%  b  75%  X  12%  c  124%  X  9% 

d  18%  X  8%  e  65%  X  10%  /  105%  X  8% 

g  27K  x  7%  ft  59%  X  11%  i  132%  X  7% 

SPECIAL  METHOD 
SIGHT  EXERCISES 

1.  Find  %  (a)  of  1%.     (6)  Of  2%.     (c)  Of  3%. 


PROCESS 


(a)  Change  1%  to  %\  %  of  %=%.  Ans. 
(6)  Change  2%  to  %\  %  of  %  =  %.  Ans. 
(c)  Change  3%  to  %  %  of  *%  =  %  =  %.  Ans. 


2.  Give  answers: 

a    %  of  1%  b  %  of  2%  c  %  of  3%  d  %  of  4% 

*    %  of  1%  /  %  of  2%  g  /4  of  3K  A  %  of  5% 

m  X  of  1%  n  X  of  1%  o  X  of  3/4  p  %  of  7% 

3.  Write  answers  from  the  book: 

a  %  of  1%     b  %  of  8%     c    %  of  9%  d  %  of  25%  e  %  of  125% 

/  %  of  2%     p  %  of  8%     h  %  of  9%  i  %  of  25%  j  %  of  125% 

fc  %  of  3%     Z  %  of  8%     m  %  of  9%  n  %  of  25%  o  %  of  125% 

p  %  of  4%     q  %  of  6%     r    %  of  7%  5  %  of  25%  t  %  of  126% 


WRITTEN  EXERCISES 

1.   A  dealer  had  four  pieces  of  cloth  containing  (a) 
57%  yd.,  (6)  57%  yd.,  (c)  57%  yd.,  and  (d)  57%  yd.,  re- 


262          WALSH'S  BUSINESS  ARITHMETIC 

spectively.     He  sold  %  of  (a),  %  of  (6),  %  of  (c),  and 
of  (c?).     How  many  yards  of  each  did  he  sell? 


PROCESS 

(a)  %  of  57%  yd.  =  19%  yd.     Ans. 

(6)  %  of  57%  yd.  =  14X2  yd.    Ans. 

Divide  57%  by  4.  This  gives  a  quotient  of  14 
(write  14),  and  a  remainder  of  1%,  or  %.  %  of  % 
is  %>.  Write  %>• 

(c)  #  of  57%  yd.  =  11%  yd.     Ans. 

Write  the  quotient  11.  Reduce  2%,  the  remain- 
der, to  %  %  of  l%  is  %.  Write  %. 

(d)  %  of  57%  yd.  =  9%  yd.     Ans. 

Write  9,  the  quotient.  Reduce  3%,  the  remain- 
der, to  %  %  of  %  is  %.  Write  %. 

TESTS 

Check  the  results  by  covering  the  answers.  In 
(a)  multiply  19%  by  3.  In  (6)  multiply  14& 
by  4.  In  (c)  multiply  11%  by  5.  In  (d)  mul- 
tiply 9%  by  6. 


2.   Write  answers  from  the  book: 

a  %  of  269%  6  K  of  374%  c  %  of  475% 

<J  K  of  598%  e  %  of  675^  /  Y,  of  750% 

g  %  of  845%  fc  %  of  932%  i  Mi  of  803% 


3.   Multiply  365%  (a)  by  1%.    (b)  by  1%.    (c)  by  1%. 


NUMBERS  AND   PROCESSES  263 


PROCESS 

(a)  365%  X  1%  (b)  365%  X  1%   (c)  365%  X 

%  73%0       Y,  5% 


457%6Ans.  438%0  Ans.  418     Ans. 

TESTS 

(a)  91%  X  5        (6)  73%0  by  6      (c)  52%  by  8. 


4.  Find  products: 

a  IX  X  157%  6  IK  X  206%  c  1%  X  314% 

<*  1%  X  408%  e   1%  X  512%  /  Itf  X  621% 

jr  IX  X  732X2  h  1%  X  815%  i  IKo  X  993% 

5.  Multiply  (a)  365%  by  4%.     (b)  257%  by  5%.     (c) 
189%  by  8£ 


PROCESS 

(a)    365%  (6)    257% 

X     4/2  X  5% 

1463    Product  by  4  1289    Product  by  5 

+  182%       "          "   %  +  85%      "          "  % 

1645%  Ans.  13741Ko  Ans. 

(c)     189% 
X     8% 
1515    Product  by  8 

+  37%        "          "  % 
1552%  Ans. 

TESTS 

Multiply  (a)  182%  by  9,  (6)  85%  X  16,  (c)  37%  by  41. 
Why? 


264          WALSH'S  BUSINESS  ARITHMETIC 
6.    Multiply  126}£  (a)  by  3%,  (b)  by  4#,  (c)  by  5%. 


PROCESS 

a)  126^  (6) 

X  3%  X    4X 

379^  Product  by  3  506    Product  by  4 

0075Xo        "         "    %  QO  72%        "          "  % 

455%  Ans.  578%  Ans. 
(c) 


632%  Product  by  5 
(X) 


702%  Ans. 

(a)  %  of  the  product  by  3  is  the  product  by  % 

(b)  %  "    "  "4 

(c)  %    "    "          " 


«  4  «     « 

«     f     {(        « 


TESTS 

(a)  Multiply  75%0  (%  of  126)0  by  6.    This  gives  >%  of  it 

(6)        "        72%   (%  "      "  )  "   8. 
(c)  70Xs  (X  "      "  )  "  10. 

l%  =  3%  3%  =  4X        5%  «  5% 


"       " 
"       " 


7.   Find  products: 


a  3%   X  126}£  b  4%   X  126%  c  5%  X  126% 

d  2%   X  126^  e  6X1  X  126%  /  7%  x  126)^ 

y  8X1  X  126^  h  9Xi  X  126X  i  2%  X  253^ 

j   3^   x  315%  fc  4%   X  407^  /  5^  X  512% 


NUMBERS  AND  PROCESSES  265 

8.   Multiply  215%  (a)  by  2%.    (6)  By  3%.    (c)  By  5%. 


PROCESS 

(a)  215%  X  2%  (b)  215%  X  3% 

646%    Product  by  3  861%  Product  by  4 

Less    53%  "   }{  Less    71%  "  % 

592  %0  Ans.  789%  Ans. 

(c)  215%  X  5% 

1292%    Product  by  6 
Less      26%  "    % 

1265%  Ans. 


9.   Multiply: 

a  8%  X  215%  b  9%  X  136%  c  7%0  X  257% 

d  3%  X  427%  e  4%  X  215%  /  5%  X  123% 

g  5%  X  224%  h  1%  X  152%  i  3%  X  306% 


SOME   SHORT  METHODS 
ALIQUOT   PARTS 

A  number  that  is  a  factor  of  another  number  is 
said  to  be  an  aliquot  part  of  the  latter. 

Thus  50^  is  an  aliquot  part  of  a  dollar;  10  days  is 
an  aliquot  part  of  a  month  of  30  days;  6  hours  is  an 
aliquot  part  of  a  day. 

Seventy-five  cents,  which  is  $%,  is  called  an  aliquant 
part  of  a  dollar,  although  it  is  an  aliquot  part  of  $3. 
While  20  days  is  not  an  aliquot  part  of  a  month  it  is 
an  aliquot  part  of  a  year. 


266          WALSH'S  BUSINESS  ARITHMETIC 

In  performing  computations,  any  number  may  be 
decomposed  into  others  that  are  aliquot  parts. 

MULTIPLYING  BY  ALIQUOT  PARTS   OF  100 

25  =  H*     12%  =  -HP-     33%  = 


16%  =  i£     50  = 

SIGHT  EXERCISES 

1.   What  is  the  cost  of  25  rugs   (a)   at  $48  each? 
(b)  At  $35  each? 


PROCESS 

(a)  At  $48  each,  100  rugs,  would  cost  48  hundred 
dollars;   %  of  100  rugs  would  cost  %  of  48  hundred 
dollars  or  12  hundred  dollars.     $1200  Ans. 

(b)  At  $35  each,  100  rugs  would  cost  35  hundred 
dollars;    %  of  100  rugs  would  therefore  cost  %  of  35 
hundred  dollars,  or  8%  hundred  dollars.     $875  Ans. 


2.  Multiply  by  25: 

a  27        b  33        c  46        d  85        e  124       /  165 
0  38        h  49        i  83        j  96        fc  169       Z  205 

3.  Multiply  by  33%: 

a  27       6  15       c  17       d  29       e  31          /  154 
#  39        h  62       z  66        j  69        fc  97  /  128 

4.  (a)  In  multiplying  48  by  12%,  what  fraction  of 
48  hundred  is  the  result?     (b)  What  is  %  of  49  hundred? 
(c)  What  number  is  equal  to  %  hundred?     (d)  To  %  hun- 


NUMBERS  AND  PROCESSES  267 

dred?     (e)  To  %  hundred?     (/)  To  %  hundred?     (g)  To 
%  hundred?     (K)  To  %  hundred?     (i)  To  %  hundred? 


5.  Multiply  by 

a  24          b  32         c  25          cZ  34         e  169         /  249 
2  44         h  69         i  89         j  51         k  321         Z  404 

6.  What  is  (a)  %  of  100?     (6)   %?     (c)  %  ?     (d)  %? 

(e)  X? 

7.  Multiply  by  16%: 

a  24         6  25         c  32         d  37        e  48        /  185 
g  19         /i  29         i  50        j   66         &  69         I  241 

WRITTEN  EXERCISES 

1.   What  is  the  cost  (a)  of  building  25  miles  of  rail- 
road at  $8765  a  mile?     (b)  Of  building  125  miles? 


PROCESS 

(a)  $8765  Divide  8765  hundred  by  4,which 
X    25               gives  2191%  hundred 

$219125  Ans.      Substitute  25  for  %  hundred 

(b)  Since  125  is  %  thousand  divide  $8765 
8765  thousand  by  8,  which  gives  X    125 
1095%  thousand.  $1095625  Ans. 
Substitute  625  for  %  thousand 


Write  answers  directly  from  the  book: 

2.   Multiply  by  25: 

a  1625   b  3463   c  2345   d  1296   e  3579   /  1143 
g  2305   h  4425   i  3617   j  1234   k  4061   I  3582 


268         WALSH'S  BUSINESS  ARITHMETIC 
3.   Multiply  by  125: 

a  1627        b  3565        c  2347  d  1298  e  5064       /  2076 

g  2316        h  3666        i  2468  j  5670  fc  4492        J  3786 

,     4.  Multiply  by  33%: 

a  1628   6  3464   c  2349  d  1297  e  4565   /  1116 

g  4538   h  4016   i  3527  j  1357  k  2348   /  3691 


6.  Multiply  by 

a  1626        6  3665        c  2248        d  1089        e  2033       /  1854 
2316        h  1444        i  1246  3458        fc  2244        J  5687 


6.  Multiply  by  16%: 

a  1629   b  3352   c  2234   d  1185   e  2468   /  1965 
g  3427   /i  2555   i  1357   j  4569   A;  3251   /  5408 


WRITTEN  EXERCISES 

1.  Mr.  Sterrett  sold  1465  shares  of  stock  in  the 
Corrigan  Paper  Mill  for  $175.25  a  share.  What  did 
he  receive? 


PROCESS 


Multiply  1465  by  25  by  taking 

1465  %  of  it.     Bring  down  25.   Find 

175.25  the  product  of  1465  by  175  by 

36625  (a)          multiplying  (a)  by  7.     Add  in 


$256,741.25  Ans.        366>  the  remaining  figures  of 
the  first  partial  product. 


NUMBERS  AND  PROCESSES  269 

2.  Multiply  by  17,525: 

a  1245   b  2467   c  3488   d  4179   e  5234  /  6432 

3.  Multiply  by  25,175: 

a  2346   6  3578   c  4569   d  5283   e  6345  /  7543 

4.  Multiply  by  7525: 

a  3457   6  4689   c  5671   d  6394   e  7456  /  8654 

5.  Multiply  by  2575: 

a  4568   b  5792   c  6783  d  7405   e  8567  /  9765 

OTHER  SHORT  METHODS 
SIGHT  EXERCISES 

1.   Find  the  cost  of  88  shares  of  stock   (a)  at  $99 
a  share,     (b)  At  $99^.     (c)  At  $99%.     (d)  At  $99%. 


PROCESS 

At  $100  a  share,  88  shares  would  cost  88  hun- 
dred dollars.  Diminish  88  hundred:  in  (a)  by  88; 
in  (b)  by  44,  Y2  of  88;  in  (c)  by  22,  #  of  88;  in  (d) 
by  11,  Y8  of  88. 


2.   Give  products: 

a  24  X  99  b  24  X  99%  c    24  X  99%  d  24  X  99% 

e   99  X  99  /   24  X  99%  g    24  X  99%  h  24  X  99% 

i    99  X  48  j  48  x  99%  A:   48  X  99%  I  48  X  99% 

m  57  x  99  n  84  X  99%  o   99  X  99%  p  66  X  99% 

g  99  x  63  r   16  x  99%  s    84  X  99%  «    88  X  99% 

M  98  X  99  o  36  X  99%  w  99  X  99%  x  72  X  99% 


270          WALSH'S  BUSINESS  ARITHMETIC 

3.   Find  the  cost  of  48  yards  of  ribbon  (a)  at 
a   yard.     (6)  At   26^.     (c)  At    13}^.      (d)  At 
(«)  At 


PROCESS 

The  price  a  yard  is  1  cent  more  than  $%  in  (a), 
than  $K  in  (6),  than  $%  in  (c),  than  $%  in  (d),  and 
than  $%in  (e). 

Add,  therefore,  48^  to  %  of  $48  in  (a),  to  %  of  $48 
in  (6),  to  X  of  $48  in  (c),  to  %  of  $48  in  (d),  and  to 
%  of  $48  in  (e). 


4.   Give  products: 


a  86  X  51 

6  88  X  13% 

c  17%  X  24 

d  36  x  34% 

e  26  X  84 

/  32  X  13X2 

flf  17%x72 

h  99  x  34% 

i  46  x  51 

j  64  X  13% 

k  17%x42 

/  69  x  34% 

m  26  x  24 

n  96  X  13% 

o  17%x54 

p  39  x  34% 

q  51  X  72 

r  72  X  13% 

s  17%x66 

t  66  X  34% 

w  28  X  26 

v  56  X  13% 

w  17%  X  78 

x  96  X  34% 

6.  What  is  the  cost  of  48  yards  of  embroidery  (a) 
at  49ff  a  yard?  (b)  At  24 jj?  (c)  At  ll^ff?  (cQ 
At  32%^?  (e)  At 


PROCESS 

The  price  a  yard  is  1  cent  less  than  $%  in  (a), 
than  $K  in  (6),  than  $%  in  (c),  than  $%  in  (d),  and 
than  $%  in  (e). 

Deduct,  therefore,  48^  from  %  of  $48  in  (a),  from 
Y4  of  $48  in  (6),  from  %  of  $48  in  (c),  from  %  of  $48 
in  (d)  and  from  %  of  $48  in  (e). 


NUMBERS  AND  PROCESSES  271 

6.   Give  products : 


a    86  X  49 

b  88  X  11% 

c    15%  X  72 

d  36  x  32^ 

e    24  X  84 

f  32  X  l\% 

g    15%  X  42 

/i  99  X  32& 

i    46  x  49 

j   64  X  UK 

fe   15%  X  24 

Z    69  x  32}£ 

m  24  X  24 

n  96  X  IV& 

o    15%  X  54 

p  39  X  32}£ 

q    72  X  49 

r  72  X  11/2 

s    15%  X  66 

<    66  x  32^ 

u    24  X  28 

v  56  X  UK 

w  15%  X  78 

z  96  X  32% 

WRITTEN  EXERCISES 

1.   Find  the  area  of  a  rectangle  344  yards  long  (a) 
99  yards  wide,  (b)  97  yards  wide,  (c)  95  yards  wide. 


PROCESS 
(o)  344  (yd.)  X  99  (yd.)     Deduct  344  from  100  times 

34056  (sq.  yd.)  Ans.     344    without    writinS    the 
latter  product. 

In  (b)  deduct  3  times  344 

from  100  times  344.  (6)  344  (yd.)  X  97  (yd.) 

Think  12   (3  X  4)  and  8         33368  (sq.  yd.)  Ans. 
(writing  8)  are  20. 

Think  12  (3x4),  14  (carrying  2)  and  6  (writing  6) 

are  20. 

Think  9  (3  X  3),  11  (carrying  2)  and  3  (writing  3) 

are  14. 

Think  1  and  3  (writing  3)  are  4.     Bring  down  3. 


2.  Multiply: 

a  456  x  99  b  98  X  375  c  576  x  999 

d  567  X  97  e  96  X  486  /  389  X  998 

g  678  X  95  h  96  X  598  i  437  X  997 

j  789  X  94  k  95  X  864  /  684  X  996 

m  234  X  98  n  97  X  864  o  886  X  995 


272          WALSH'S  BUSINESS  ARITHMETIC 

3.  At  $248  an  acre,  find  the  cost  (a)  of  37%  acres, 
(6)  Of  35  acres,  (c)  Of  27%  acres,  (d)  Of  26%  acres, 
(e)  Of  75  acres,  (/)  Of  87%  acres,  (g)  Of  97%  acres, 
(h)  Of  62%  acres. 


PROCESS 

(a)     25    A.  $6200  (6)     25    A.     ? 

+    12%  "      ?  +10     "      ? 


37%  A.     ?      Ans.  35    A.     ?    Ans. 

(c)     25    A.     ?  (d)     25    A.     ? 

+      2%  "      ?  +     IX    "      ? 


27%  A.     ?      Ans.  26%  A.     ?    Ans. 

(e)   100    A.     ?  (/)   100    A.     ? 

-    25      "      ?  -    12%  "      ? 


75    A.     ?      Ans.  87%  A.     ?    Ans. 

(g)  100    A.     ?  (h)     50    A.     ? 

-      2%  "      ?  +    12%   "      ? 


97%  A.     ?      Ans.  62%  A.     ?    Ans. 

In  (a)  find  the  cost  of  12%  A.  by  taking  %  the  cost 
of  25  A. 

In  (b)  find  the  cost  of  10  A.  by  multiplying  $248  by  10. 
In  (c)  the  cost  of  2%  A.  is  Mo  the  cost  of  25  A. 

etc. 


4.   Multiply: 

a  136  x  37%  b  212  X  75  c  384  X  87% 

d  444  X  43^  e  516  x  35  /  639  X  66% 

0  712  X  62%  h  883  X  45  i  969  X  76% 

j  842  X  47%  &  715  X  97  J  624  X  17% 


NUMBERS  AND  PROCESSES  273 

5.   Find  the  cost  of   13471  yards    of    prints   (a)   at 
cents  a  yard.     (6)  At  10%  cents. 


METHOD 

Save  time  and  figures  by 
and  of  %. 

using  aliquot  parts   of    %6 

(a) 
Atl 

/ 

1347^ 

(6)           1347K 

1^  $161.22tf 

%t        6.73%   (I) 
^          84%2  (II) 

At  10^  $134.75 
"    %          3.36%       (III) 
"    X         1.68^6      (IV) 

$168.80  Ans. 

$139.80  Ans. 

For 

(II)  take  Y8  of  (I) 

For  (IV)  take  }{  of  (III) 

6.   Find  products : 


a  2%   X  484 
d  3%  X  576 
g  4%>  X  328 
j   5Ke  X  254 

6  6%j  X  184 
e  7%   X  908 
h  8%  X  736 
k  9%  X  864 

c  10%  x  272% 
/  18%   X  104/2 
i  12%  x  364% 
1  16J4,  X  406^ 

DECIMALS 

ONE  DECIMAL  FACTOR 
WRITTEN  EXERCISES 

1.   What  is  the  area  of  a  plot  (a)  7  rods  long  6.85 
rods  wide?     (b)  15  rods  long  8.4  rods  wide? 


METHOD 

(a)     6.85  (rd.)  (6)      8.4  (rd.) 

X  7    "  X  15      " 

Ans.  47.95  (sq.  rd.)  Ans.  126.0  (sq.  yd.) 

When  the  product  can  be  written  at  once,  insert 
the  decimal  point  when  it  is  reached  in  performing 
the  multiplication. 


274          WALSH'S  BUSINESS  ARITHMETIC 

2.   Write  answers  from  the  book: 

a  8  X  13.52  b  12  X  2.345  c  32  X  .0204 
d  6  X  2.345  e  15  X  12.34  /  13  X  120.5 
g  5  X  .1768  h  21  X  3.421  i  16  X  24.31 

SIGHT  EXERCISES 

1.  Multiply  by  10: 

a  34.26      b  4.32      c  .897     d  .0345      e  .0059     /  4.6 
g  19.84     h  5.67     i  .603     j   .0567     &  .0006     I  5.2 

2.  Multiply  by  100: 

a  62.43      6  9.84      c  .789      d  .0534      e  .0095     /  6.4 
g  35.18     A  5.23     i   .264     j   .0402     k  .0007     /  8.3 

3.  Multiply  by  1000: 

a  26.43      6  8.49      c  .978      d  .0435      e  .0062    /  5.7 
g  17.09     A  3.46     i   .104     j   .0926     &  .0004     I  9.1 

WRITTEN  EXERCISES 

1.  The  coin  value  of  a  franc  is  $.193.  What  is  the 
value  (a)  of  10  francs?  (6)  Of  20  francs?  (c)  Of  60 
francs? 


PROCESS 

(a)  To  multiply  $.193  by  10,  shift  the  decimal 
point  one  place  to  the  right.  For  (b)  multiply  by 
2  the  result  obtained  in  (a). 


NUMBERS  AND  PROCESSES  275 

2.  Write  answers  from  the  book: 

a  40  X  3.1416  b  $4.8665  X  100  c  70  X  2.345 
d  50  X  .1975  e  .3937  X  200  /  80  X  13.81 
g  60  X  123.4  h  2.2046  X  300  i  90  X  347.2 

3.  (a)  How  many  pounds  are  there  in  900  kilos  of 
2.2046  pounds  each?     (b)  Find  the  coin  value  of  £4000 
at  $4.8665  to  the  £. 


METHOD 

(a)     2/20.46  lb.  (b)     $4/866.5 

X 


1984.14  lb.  Ans.  $19466.0    Ans. 

In  (a),  multiply  2.2046  by  100  by  shifting  the  deci- 
mal point  two  places  to  the  right.  Multiply  the 
changed  multiplicand  by  9. 

In  (b)  multiply  4.8665  by  1000  by  shifting  the  deci- 
mal point  three  places  to  the  right.  Multiply  the 
changed  multiplicand  by  4.  Cancel  the  decimal 
cipher. 


4.   Multiply.     Test: 

a  900  X  174.9862  b  1200  X  14.756  c  700  X  1374.64 
d  2400  X  .02345   e  600  X  24.385  /  3000  X  3.0098 

MULTIPLYING  DECIMALS 
WRITTEN  EXERCISES 

1.   Multiply  (a)  .243  X  .37.     (b)  3.65  X  "8.6. 
Changing   the   decimals   to   common   fractions   the 
problem  becomes 


276          WALSH'S  BUSINESS  ARITHMETIC 
243        37          8991 

x  wo-          =-0899lAns- 


The  numbers  of  ciphers  in  the  denominator  of  the 
product  is  equal  to  the  combined  number  in  both 
factors. 


PROCESS 

Ignoring  the  decimal  points,  multi- 
ply 243  by  37.    Since  there  are  three 
*  decimal  places  in  the  multiplicand 

729  and  two  in  the  multiplier,  point  off 

.08991  Ans.     five  (3  +  2)  decimal  places  in  the 
product.    To  point  off  this  number, 
prefix  a  decimal  cipher  to  the  original  product. 

(6)     3.65 

(6)  Cut  off  3  decimal  places.  X  8  6 

Cancel  the  terminal  cipher  2920~ 

31.890  Ans. 

TEST 

As  a  preliminary  to  the  test  of  (b)  note  that  the 
product  must  be  more  than  8  times  3  and  less  than 
9  times  4. 


2.   Find  products.     Test: 

a  7.29    X  4.8      b  7.0234  X  819      c  25.09    X  8.32 
d  .0385  X  7.2      e  6.1408  X  .042    /  531.75  X  .484 


NUMBERS  AND   PROCESSES  277 

3.   Multiply   513.583    (I)    by   3.25,    (II)    by   23.25, 
(III)  by  37.5 


METHOD 

(I)  a     513.583  X  3.25 

b     128.39575  Product  by  % 

Ans.      1669.14475  "       of  (a  by  3)  +  b 

In  doing  the  work  substitute  %  for  .25 

(II)  513.583  When  the  multiplier  is  a  mixed 

23.25      decimal  containing  such  deci- 

128  39575       ma^s  as   *^>   •^^'   etc*>   some 

1540  749  accountants  prefer  to  place  the 

10271  66  latter  beyond  the  last  figure 

of  the  multiplicand,   as   they 

do  in  writing  a  mixed  number.     In  this  case  they 

insert  the  decimal  point  in  each  partial  product. 

(III)  a  513.583  X  37.5  (300/8) 

b  154074.9        Product  of  a  by  300 
19259.3625  "b    "  % 

Test  by  using  aliquot  parts,  multiplying  first  by  25, 
then  by  12%. 


4.   Multiply: 

a  .864  X  .625  b  84.624  X  S3%  c  78.6  x  .135 

d  97.25  X  .23  e  14.9375  x  34%  /  437  X  .995 

g  27.055  x  3.4  h  8312.34  X  .99  i  .115  x  6.288 

j  .875  x  3.08  k  99.7  x  6.086  /   95.704  X  32} 

m  88.5  X  .6248  n  74.2  X  .375  o  437.6  x  .099 

p  18.75  X  2.94  q  63.8  X  .0495  r  28.4  X  .076 


278         WALSH'S  BUSINESS  ARITHMETIC 

MULTIPLYING  DENOMINATE  NUMBERS 
WRITTEN  EXERCISES 

1.   How  many  bushels  of  apples  are  there  in   15 
barrels  averaging  2  bushels  3  pecks  each? 


METHOD 


2bu.  3pk.        Think  45  pk.     (15  X  3  pk.),  11  bu. 
15  1    pk.     (changing  to   bushels   and 

pecks).     Write  1  pk. 


bu.  1  pk. 
(carrying  11  bu.)    Write  41  bu.    Ans.  41  bu.  1  pk. 


2.   Write  answers  from  the  book: 

a  3  Ib.  9  oz.      b  8  bu.  2  pk.      c  4  pk.  3  qt.      d  5  gal.  3  qt. 
X4  X3  X6  X5 


e  £4  8s.  /  5s.  6d.  g  6  qt.  1  pt.       h  3  ft.  4  in. 

X7  X8  X9  XlO 


3.  A  family  uses  2  quarts  1  pint  of  milk  a  day. 
How  much  does  it  use  (a)  in  a  week?    (b)  During  June? 

4.  Write  products  from  the  book: 

a  3  Ib.  10  oz.     b  3  qt.  1  pt.       c  3  yd.  1  ft.       d      46s. 
X  18  X  16  X  24  X  12 


e  10s.  6d.         /  1  bu.  3  pk.      g  3  pk.  4  qt.      h  2  ft.  6  in. 
X  18  X  20  x  15  x  40 


CHAPTER  NINE 

DIVISION 
DIVIDING  BY  AN  INTEGER 

SIGHT  DRILLS 


A 

B 

C 

D 

E 

F 

G 

H 

a  45 

54 

102 

104 

105 

106 

108 

140 

b  56 

65 

110 

111 

114 

116 

117 

143 

c  69 

76 

118 

119 

120 

121 

123 

144 

d  78 

87 

125 

126 

128 

130 

132 

145 

e  86 

98 

133 

135 

135 

136 

138 

147 

1.  Name  rapidly  (I)  by  columns,  (II)  by  lines,  the 
multiples  (a)  of  2.     (b)  Of  4.     (c)  Of  8.     (d)  Of  3. 
(e)  Of  9.     (/)  Of  6.     (g)  Of  5.     (h)  Of  7.     (i)  Of  11. 

2.  State  (I)  by  columns,  (II)  by  lines,  the  remainders 
when  the  following  numbers  are  divided:    (a)   By  3. 
(6)  By  5.     (c)  By  9.     (d)  By  11.     (e)  By  4.     (/)  By  8. 
(<7)  By  25. 

ABCDEFGH 

a  345  554  102  504  905  506  109  543 
b  656  165  210  611  814  416  217  677 
c  469  987  325  729  623  321  423  709 
d  278  887  425  826  735  239  332  821 

3.  Give  two  factors  of: 

a  65    b  69    c  86    d  133  e  106  /  111 

0  87    h  46    i  57    j  119  k  143  I  121 

m  51     n  95     o  62    p  145  q  134  r  118 

s  93    *  58    M  91     v  158  w  155  *  146 

279 


280          WALSH'S  BUSINESS  ARITHMETIC 

ORAL  PROBLEMS 

1.  In   how  many   weeks   will   a   man   earn   $1440 
when    his    weekly    earnings    are    (a)  $15?     (b)  $16? 
(c)  $18?     (d)  $24?     (e)  $30?     (/)  $36? 

2.  How   many    pounds    are   there   in    (a)    96    oz.? 
(b)  144  oz.?     (c)  80  oz.?     (d)    112  oz.?     (e)  176  oz.? 
(/)   128  oz.? 

3.  How    many    feet    are    there    in    (a)    132    in.? 
(b)  168  in.?      (c)  96   in.?      (d)  192  in.?     (e)  288  in.? 
(/)  960  in.? 

4.  (a)  At  60  pounds  to  the  bushel,  how  many  bushels 
of  potatoes  weigh  9600  pounds?     (b)  How  many  bushels 
of  oats,  weighing  32  pounds  to  the  bushel,  will  have 
the  same  weight? 

SIGNS   OF  DIVISION 

To  indicate  that  15  is  to  be  divided  by  3,  write  3, 
o\  -I  *       the  divisor,  then  a  curved  line,  then  the 
dividend.     Write  5,  the  quotient,  under- 
neath.    This  form  may  be  read  "3  into  15 
(goes)  5  times." 

Or,  write  the  dividend  above  a  line  and  the  divi- 
sor   underneath.     Follow  with   a   sign   of       -  ~ 
equality  and  then  the  quotient.     This  form        -  =  5 
may  be  read  "15  over  3  equals  5." 

Or,  write  the  dividend,  then  the  division  sign  (-s-), 

then  the  sign  of  equality,  concluding 

15  -j-  3  =  5    with  the  quotient.     This  form  is  read 

"15    divided    by    3    equals    5."     The 

other  two  forms  may  also  be  read  in  this  way. 

The  second  form  is  generally  employed  when  either 
term  is  compound  or  contains  literal  numbers. 


NUMBERS  AND  PROCESSES  281 

3X  16        ab        y2-  16 
2  c  '         y  +  4 

In  many  European  countries  the  colon,  which  in 
this  country  is  employed  to  denote  ratio,  is  used  as 
the  division  sign.  In  some  of  them  our  division  sign 
(-T-)  indicates  subtraction. 

SHORT  DIVISION 
WRITTEN  EXERCISES 

1.  (a)  When  15  barrels  of  sugar  weigh  4620  pounds,, 
what  is  the  average  weight  per  barrel?  (6)  How 
many  overcoats  at  $15  each  will  cost  $5250? 


PROCESS 

(a)  15)4620  Ib.  Divide  4620  Ib.  by  15,  the 

Ans.  308  Ib.  number  of  barrels. 

(6)  $15)$5250  Divide  $5250  by  $15,  the 

Ans.  350  (coats)  cost  of  a  coat.  The  quo- 
tient, 350,  is  the  number  of 

coats.     Write  coats  in  a  parenthesis. 

Test  each  result,  covering  the  dividend  with  a 
strip  of  paper  on  which  you  write  the  product  of 
the  quotient  by  the  divisor.  Remove  the  paper 
and  compare  this  product  with  the  dividend. 


Be  careful  to  place  the  first  quotient  figure  under 
the  right-hand  figure  of  its  partial  dividend,  and  to 
place  a  quotient  figure  or  cipher  under  each  remaining 
figure  of  the  dividend. 

2.  Write  quotients  from  the  book.  Under  each 
write  its  product  by  the  divisor: 


282          WALSH'S  BUSINESS  ARITHMETIC 
a  32)1024  b  18)5418  c  15)3600  d  19)4408 

e  21)2331  /  14)2002  g  13)3952  h  17)8517 

i  16)2128  j  24)2952  k  23)7590  I  25)5375 

DIVIDING  BY  A  MULTIPLE   OF  10 
PREPARATORY  EXERCISES 

1.  At  $200  an  acre  how  many  acres  of  land  will 
cost  $2800? 

2.  At  2000  pounds  to  the  ton,  how  many  tons  are 
there  in  86000  pounds  of  coal? 

3.  At  160  square  rods  to  the  acre,  how  many  acres 
are  there  in  3200  square  rods? 

4.  (a)  Why  is  the  quotient  of  2800  -f-  200  the  same  as 
the  quotient  of  28-7-2?     (b)  By  what  number  are  both 
terms  of  2800  -=-  200  divided  to  change  them  to  28  -T-  2? 


Dividing  the  divisor  and  the  dividend  by  the  same 
number  makes  no  change  in  the  quotient. 


WRITTEN  EXERCISES 

1.  (a)  At  $60  each,  how  many  cows  will  cost  $57,600? 
(b)  What  is  the  average  cost  of  a  rug  when  $52,000  is 
paid  for  800  rugs? 


METHOD 
(a)  6 1 0)6760 10  (b)  8 1 00)$520|00 

(cows)  Ans.  $  Ans. 

In  (a)  divide  both  terms  by  10  by  cutting  off  the 
final  cipher.     Divide  5760  by  6. 
In  (b)  divide  both  terms  by  100  by  cutting  off  the 
last  two  ciphers.     Divide  $520  by  8. 


NUMBERS  AND  PROCESSES  283 

2.   Write  quotients  from  the  book: 

a  120)67,800  b  800)36,800  c  1500)106,500 

d  600)45,600  e  160)38,560  /  4000)292,000 

REMAINDERS 
PREPARATORY  EXERCISES 

1.  At  $16  each,  how  many  calves  can  be  bought  for 
$500,  and  how  much  money  will  remain? 

2.  At  $16  a  ton,  how  much  iron  ore  can  be  bought 
for  $500?     Give  answer  as  a  mixed  decimal. 

3.  How  many  miles  an  hour  does  a  train  travel 
when  it  goes  500  miles  in  16  hours?     Give  answer  as 
a  mixed  number. 

4.  If  a  vessel  goes  16  miles   an  hour,  how  many 
hours  and  minutes  will  it  require  to  go  500  miles? 

5.  How    many    persons    can    be    properly    accom- 
modated in  a  room  having  500  square  feet  of  floor 
space  if  each  is  to  have  at  least  16  square  feet? 

6.  How  many  auto  cars  are  needed  to  transport  500 
soldiers  at  one  time  if  each  can  carry  only  16  soldiers? 

7.  Why  should  the  remainder  be  given  in  the  answer 
to  Ex.  1  and  omitted  in  the  answer  to  Ex.  5? 

8.  What  is  done  with  the  remainder  in  the  answer 
to  Ex.  6? 

WRITTEN  EXERCISES 

1.   Write  answers  from  the  book,  giving  each  quo- 
tient as  an  abstract  number  and  the  remainder  as  a 
concrete  number: 
a  17  lb.)8523  Ib.          b  $14)$4258  c  16  T.)8163  T. 


d  15  yd.)4539  yd.        e  13  mi.)7973  mi.         /  24  A.)7227  A. 


284          WALSH'S  BUSINESS  ARITHMETIC 

2.  At  2000  pounds  to  the  ton,  give  the  number  of 
tons  and  pounds  (a)  in  96,875  pounds  of  coal,  (b^ 
In  97,000  pounds,  (c)  In  97,450  pounds. 


METHOD 

(a)  2|000lb.)96|875lb. 

48(T.)875  Ib.  Ans. 

When  96875  Ib.  is  divided  by  1000,  there  is  a 
remainder  of  875  Ib.  Write  this  remainder  after 
48,  the  quotient  of  96  (thousand)  divided  by  2 
(thousand).  After  48,  the  number  of  tons,  write 
T.  in  a  parenthesis. 

(6)  2|QOOlb.)97lOOOlb. 

48 (T.)  1000  Ib.  Ans. 

2  (thousand)  is  contained  in  97  (thousand)  48 
times  with  a  remainder  of  1  (thousand) 

(c)  2|000lb.)97|450lb. 

48 (T.)  1450  Ib.  Ans. 

Divide  97  by  2,  writing  48,  the  quotient.  Prefix 
1,  the  remainder,  to  450,  the  figures  of  the  dividend 
that  are  cut  off. 


To  divide  an  integer  by  a  number  ending  in  one  or  more 
ciphers  cut  off  the  terminal  cipher  or  ciphers  in  the  divisor 
and  the  same  number  of  figures  from  the  right  of  the  divi- 
dend. Divide  the  remaining  figures  of  the  dividend  by  the 
remaining  figures  of  the  divisor.  Write  as  the  remainder 
the  figures  of  the  dividend  that  have  been  cut  off,  prefixing 
the  partial  remainder,  if  any,  left  after  performing  the 
division. 


NUMBERS  AND  PROCESSES  285 

3.   Find  quotients  and  remainders: 
a  120)57650  b  700)50200  c  1800)203500 

d  210)25635  e  140)48320  /  3200)99805 

DECIMAL   QUOTIENTS 

When  the  quotient  of  two  integers  is  to  be  given  as 
a  decimal,  continue  the  division  by  mentally  annexing 
decimal  ciphers  to  the  dividend. 

WRITTEN  EXERCISES 

1.  (a)  I  paid  $18  for  8  bushels  of  potatoes;  what 
was  the  cost  a  bushel?  (b)  At  $16  a  ton,  how  many 
tons  of  straw  can  be  bought  for  $250? 


PROCESS 

Place  a  decimal  point  after 

(a)  8)$18.  $18.     Place  a  decimal  point 

$  2.25  Ans.  m   the   quotient   under   the 

one  in  the  dividend. 

Place  a  decimal  point  after 

(b)  16)250  ®^'    ^°  not  wr*te  ^e  deci- 

— — * ,  mal  ciphers.    Place  a  decimal 

'  Ans>  point  in  the  quotient  under 
the  one  in  the  dividend. 


2.   Write  quotients  from  the  book,  as  mixed  deci- 
mals: 

a  12)246  b  8)243  c  16)340  d  4)3926 

e  14)175  /  6)201  g  18)405  h  2)4321 


286          WALSH'S  BUSINESS  ARITHMETIC 

DECIMAL  DIVIDENDS 

3.   Divide  (a)  24.3  by  8.     (b)  .246  by  12. 


PROCESS 

(a)  8)24.3  (6)  12) .246 

3.0375  .0205 

Place  a  decimal  point  in  the  quotient  under  the 
one  in  the  dividend.  In  (b)  place  a  cipher  under 
the  2  in  the  dividend. 


4.  Write  quotients  from  the  book: 

a  12)36.6  6  8)3.23  c  16). 344  d  9)34.2 

e  12)4.86  /  8). 324  g  18)3.69  h  4)1.02 

5.  How  many  tons  are  there  (a)  in  96,875  pounds? 
(b)  In  97,000  pounds?     (c)  In  97,450  pounds?     Give 
results  as  mixed  decimals. 


METHOD 

(a)  gppp)96.875/  (6)  2PPP)97.PPP/ 

Ans.  48.4375  (T.)  48.5  (T.) 

(c)  2PPP)97.450/ 
Ans.   48.775  (T.) 

Since  the  answer  is  to  be  given  as  a  decimal,  cancel 
the  three  ciphers  in  the  divisor  (dividing  it  by  1000) 
and  divide  each  dividend  by  1000  by  setting  off 
three  decimal  places. 


NUMBERS  AND  PROCESSES  287 

To  show  that  the  original  dividend  is  an  integer, 
place  after  it  a  decimal  point,  and  cancel  it  when  the 
new  one  is  written. 

6.  How  many  tons  are  there  in  14,760  pounds? 

7.  At  160  square  rods  to  the  acre,  how  many  acres 
are  there  in  2440  square  rods? 

8.  Express  quotients  in  decimal  form: 

a  120)426     b  800)1244      c  16000)4040     d  160)808 

9.  Divide  (a)  62.4  by  120,  (b)  14.84  by  16000. 


METHOD 

Divide  the  divisor  by  10  by  canceling  the  cipher. 

(a)  120)6.2/4  Divide  the  dividend  by  10  by 

- —  moving  the  decimal  point  one 

Ans'   place  to  the  left.     Divide  the 
changed  dividend  by  the  changed  divisor. 

To   move   the   decimal   point   in    the   dividend 

three  places  to  the  left,  prefix 

(b)  16W).014/84 


10.  Express  quotients  in  decimal  form: 

a  300)4.26         b  6000)524.4       c  150). 606         d  90)47.7 

FRACTIONAL   QUOTIENTS 

When  the  result  of  a  division  is  to  be  expressed  as 
a  mixed  number,  write  the  remainder  over  the  divisor 
in  the  form  of  a  fraction. 

11.  Express    each    quotient   as    a    mixed    number. 
Write  answers  from   the   book. 

a  11)37561         b  13)29400         c  12)39863         d  15)46702 


288          WALSH'S  BUSINESS  ARITHMETIC 

12.   In  the  following  give  the  fraction  in  the  quotient 
in  lowest  terms.     Write  answers  from  the  book. 

a  14)30107         b  16)50100         c  21)84639         d  18)90372 


COMPOUND   NUMBER    QUOTIENTS 

The  result  of  the  division  of  a  denominate  number 
by  an  abstract  number  may  be  expressed  as  a  com- 
pound number,  as  shown  by  the  first  example  (a)  below. 

13.  Divide  (a)  54  bushels  by  16.  (b)  42  yd.  2  ft. 
3  in.  by  9. 


PROCESS 

54  bu.  divided  by  16  gives  a  quotient  of  3  bu. 
with  a  remainder  of  6  bu.     Change  the  latter  to 

/  \  I*\KA  u  24  pk.      This  divided 

(a)  16)54  bu.  *       . 

by  16  gives  a  quotient 
Ans.  3bu.lpk.4qt. 


mainder  of  8  pk.  Change  the  latter  to  64  qt. 
This  divided  by  16  gives  a  quotient  of  4  qt. 

After  dividing  42  yd.  by  9,  and  writing  the  quo- 
tient, 4  yd.,  change  6  yd.,  the  remainder,  to  18  ft. 

(6)  9)42  yd.  2  ft.  3  in.  To  th/s  add  2  'V  .™ak; 

ing  the  next  dividend 
Ans.  4  yd.  2  ft.  3  in.  2Q  ft      Wrfte  %  ft>>  ^ 

quotient,  and  change  the  remainder,  2  ft.,  to  24  in. 
To  this  add  3  in.,  making  the  next  dividend  27  in. 
Write  3  in.,  the  next  quotient. 


14.   Express  each  quotient  as  a  compound  denomi- 
nate number.     Write  answers  from  the  book. 


NUMBERS  AND  PROCESSES  289 

a  8)34  Ib.        6  6)39  Ib.  6  oz.       c  12)51bu.  2  pk.  4  qt. 
d  9)40  yd.       e  7)33  gal.  1  qt.     /  10)95  yd.  1  ft.  10  in. 
g  8)37  bu.       h  5)63  yd.  1  ft.       i  11)86  gal.  2  qt.  1  pt. 

15.   Divide  65  yd.  10  in.  by  10. 


METHOD 

10)65  yd.  0  ft.  10  in.      Insert  the  missing  denomi- 
nation. 


16.   Express  quotients  as  compound  numbers, 
a  10)62  yd.  8  in.        b  12)76  bu.  4  qt.       c  9)73  gal.  1  pt. 


FRACTIONAL  DIVIDENDS 

SIGHT  EXERCISES 
1.   Give  quotients. 


a    % 

-s-  2 

b    % 

-5-  2 

c 

IX  + 

2 

d 

1/5 

-f-  2 

e    % 

-5-  3 

f    % 

-H  3 

<J 

2/4^ 

S 

h 

1% 

-3 

i    % 

-5-2 

i  % 

-5-2 

k 

w  + 

2 

I 

1% 

-  2 

m  % 

-r-   5 

n  l% 

-5 

0 

3K  -^ 

5 

P 

2/2 

-  5 

q    % 

-5-  4 

r   *% 

—  4 

s 

W-  + 

4 

t 

3/5 

-5-  4 

Dividing 

the 

numerator 

divides 

a 

fraction 

• 

2.   Give  answers : 

a  %  of  /2  =  ?         6  %  of  %  =  ?         c  K  of  IX  =  ? 


Multiplying  the  denominator  divides  a  fraction. 


290 


WALSH'S  BUSINESS  ARITHMETIC 


3.   Give  quotients: 


a  X  +  2 

6  %  -^  3 

*'  X  +  5 

m  %  -5-  4 

<7  %-  6 


-  3 

-h  5 

+  4 

-=-  6 


C  1%    -5-    2 

<7  2%  -s-  3 

fr  IV    •    ^ 

A/  J-/3      ~*~      *^ 

o  1%  -i-  4 

s  1%  4-  6 


d  IK  -s-  2 

A  2%  -5-  3 

Z    3%  4-  5 

p  3%  -s-  4 

<    4%  *  6 


WRITTEN  EXERCISES 

1.  A  farmer  raised  1865%  bushels  of  potatoes  on 
7  acres,  (a)  What  was  the  average  yield  an  acre? 
(b)  Divide  1765%  by  8. 


METHOD 


(a)  7)1865%bu.  Change  the  remainder,  3%, 

266%  bu.  Ans.     to    the    improper    fraction, 


(b)  8)1765% 


Change  the  remainder  5% 

to%     1X-8=% 


2.   Divide.     Write  answers  from  the  book: 
a    9)3087%,  b  8)4456%  c  7)5005%  d  6)2352% 

0  3)9423%  h  2)8932% 

k  5)4767%  Z    6)38732< 

o  9)4627%  p  8)598S5i 


e    5)6095% 
t    3)7345% 

m  7)2986% 


/  4)7348% 
j  4)6934% 
n  8)3597% 


In  dividing  a  mixed  number  by  an  integer  divide 
the  fractional  remainder  by  the  divisor  when  the 
quotient  is  to  be  expressed  as  a  mixed  number. 


NUMBERS  AND  PROCESSES  291 

DIVIDING  BY  FACTORS 
WRITTEN  EXERCISES 

1.  A  farmer  delivered  55,104  pounds  of  corn  to  a 
dealer.  (a)  How  many  bushels  were  there  at  56 
pounds  to  the  bushel?  (b)  Find  its  value  at  $1.47^ 
a  bushel. 


METHOD 

8)55,104  Instead    of    dividing    by 

.  7)  6888  &6>  many  accountants  use 

Ans.    984  (bu.)  the  factors.     Test  the  re- 

sult by  covering  the  divi- 
dend, and  writing  the  product  of  984  by  8,  and 
this  product  by  7. 


2.   Find  quotients: 

a  59,544  ^72  b  68,096  -=-  64  c  91,584  -*•  96 

d  99,616  -f-  88  e  88,816  -  56  /  78,197  +  49 


3.   Divide  (a)  86,347  by  91     (6)  228,338  by  66. 


METHOD 

(a)     7)86,347  (b)  11)228,338 

13)12,3352/7  6)20,758 

948%  Ans.  3459%  Ans. 


292         WALSH'S  BUSINESS  ARITHMETIC 

4.  Express  quotients  as  mixed  numbers: 

a  68,551  -.  81  b  81,745  -  66  c  95,239  -j-  54 

d  83,015  ^42  e  90,583  -  39  /  71,229  -  28 

Decimal  quotients  are  frequently  limited  to  two  or  to  three  places.  In 
such  a  case  carry  out  the  result  to  an  additional  place.  When  this  last 
quotient  figure  is  less  than  5,  reject  it  in  stating  the  result;  when  it  is 
5  or  more  use  it  to  increase  the  preceding  figure  by  1. 

5.  Divide  (a)  34,885,  (b)  24,703  by  96,  giving  quo- 
tients to  nearest  thousandth,  to  nearest  hundredth. 


METHOD 

(a)     8)34,885  (b)  8)24,703 

12)4360.625  12)3087.875 
363.3854  257.3229 

(I)  Quotient  to  nearest  thousandth 
(a)  363.385  Ans.     (b)  257.323  Ans. 

(II)  Quotient  to  nearest  hundredth 
(a)  363.39  Ans.     (6)  257.32  Ans. 


6.  Give  quotients  (I)  to  nearest  thousandth,  (II)  to 
nearest  hundredth. 

a  58,843  *  48  6  45,678  -r  72  c  62,943  -  77 

d  37,945  -r-  56  e  86,745  4-84  /  76,849  -j-  63 

7.  Divide   (a)   86,347   by   91,    (b)  228,338   by   66; 
(I)  expressing  each  result  as  a  mixed   number,   (II) 
giving  quotients  and  remainders. 


NUMBERS  AND  PROCESSES  293 


METHOD 

(a)  7)86,347  (b)  6)228,338 
13)12,335%  11)38,056^ 

(I)  948%  Ans.  3459%  Ans. 

(II)  948;  rem.  79  Ans.  3459;  rem.  44  Ans. 

In  (a),  the  denominator  of  %,  the  fraction  in 
the  mixed  number  quotient  (I),  being  the  same  as 
the  regular  divisor,  91,  write  79,  its  numerator,  as  the 
remainder  in  (II). 

In  (b)  multiply  %,  the  fraction  in  the  answer  (I) 
by  66,  the  regular  divisor,  which  gives  44  as  the 
remainder  (II). 

By  omitting  to  reduce  the  fractions  %  and  %  to 
lowest  terms,  the  denominator  of 

(b)  6)228,338         the  latter  would  correspond  with 

11)38,056%      the  regular  divisor,  and  its  numer- 
3459%      ator  would  be  the  remainder. 


8.   Divide;  (I)  expressing  results  as  mixed  numbers, 
(II)  giving  quotients  and  remainders. 


a  68,551  •*-  81 
d  34,672  -5-  77 
g  11,572  -f-  33 
j  48,312  -s-  42 

b  83,015  +  42 
e  53,219  4-  32 
h  81,745  *  66 
k  42,094  +  84 

c  94,724  ^  48 
/  95,239  -*-  54 
i  96,583  -*-  39 
I  71,229  *  28 

DIVIDING  BY  MULTIPLES 
PREPARATORY  EXERCISES 

1.  At  $1J£  each  what  will  be  the  cost  of  12  baseballs? 

2.  How  many  baseballs  costing  3  half  dollars  each 
an  be  bought  for  36  half  dollars? 


294         WALSH'S  BUSINESS  ARITHMETIC 

3.  (a)  3  halves)36  halves        (b)  IX)  18         (c)  3)36 

?  ?         T 

4.  (a)  How  many  times  IX  is  3?     (6)  How  many 
times  18  is  36?     (c)  How  does  the  quotient  of  18  •*•  IX 
compare  with  the  quotient  of  36  +  3? 


Multiplying  the  divisor  and  the  dividend   by  the  same 
number  makes  no  change  in  the  quotient. 


5.   How  many  baseballs  can  be  bought  for  $6  when 
they  cost  (a)  $X  each?     (6)  $M  each? 


METHOD 

(a)       X)     6  (b)       }{}     6 

X 2X 2  X  4X  4 

1)    12  1)  24 

Although  you  obtain  the  result  in  (a)  by  multi- 
plying 6  by  2,  and  in  (6)  by  multiplying  6  by  4,  you 
should  realize  that  you  are  really  dividing  $6,  the 
sum  to  be  spent,  by  the  cost  of  each,  by  $X  or  $& 
respectively,  to  ascertain  the  number  that  can  be 
purchased. 


6.   Give  quotients: 

a  X)24  b  X)36  c  Xm  d  X)144 


JQ31  0  X)72  h  X)140 

j  X)33 


NUMBERS  AND  PROCESSES 

WRITTEN  EXERCISES 


295 


1.   How   many   baseballs   can   be   bought   for   $15 
when  the  price  is  (a)  $%  each?     (6)  $lji  each? 


(a)       JO  15 
X4  X4 


METHOD 

(&)     IK)  15 
X4  X4 


3)   60 

20  (baseballs)  Ans. 


5)   60 

12  (baseballs)  Ans. 


Multiply  the  divisor  and  the  dividend  by  the 
denominator  of  the  fraction.  Divide  the  new 
dividend  by  the  new  divisor.  Test  (a)  by  multiply- 
ing •%  by  20;  (6)  by  multiplying  1%  by  12. 

In  practice  omit  such  unnecessary  figures  as  the 
multipliers  shown  above.     Write  only 

(a)  JQ  15  (6)  IK)  15    . 

3)60  5)60 


2.   Find    quotients.     Write    answers    directly    from 
the  book: 

b  /4 


a  fc 

3.   Divide.     Test: 

a  l/2)112/2  6  DQ236/4 

g  2)0242/3  h  2^)231% 


i  2/5)200/5 


296         WALSH'S  BUSINESS  ARITHMETIC 

4.   At  $7%  a  ton,  how  many  tons  of  coal  can  be 
bought  (a)  for  $324?     (6)  For  $318%? 


METHOD 

(a)  7)0824  (b)  7^)318% 

15)648  15)637^ 

43}£  (T.)  Ans.  42^  (T.)  Ans. 


5.   Divide.     Test: 

a  IflllOX  b  1?Q108X 


d  1J0120X  «  IK)  1^3%  /  2)0163% 

6.   Divide  83647  by  65.     Give  quotient  (a)  correct 
to  nearest  hundredth,     (b)  As  a  mixed  number. 


METHOD 


Multiply    the   divisor   and 
65)83,647  the   dividend  by   2.     Cancel 

13P)  16,729.4  the  cipher  in  the  divisor  and 

1286.88  Ans.        cut  off  one  decimal  place  in 
the  dividend. 


7.  Divide  by  35,  giving  the  result  correct  to  the 
nearest  hundredth : 

a  17,463       6  23,986      c  35,207  d  43,916      e  54,268 

8.  Divide  by  45,  giving  the  quotient  as  a  mixed 
number: 

a  63,482       b  74,006       c  82,954  d  96,875       e  83,108 


NUMBERS  AND  PROCESSES  297 

9.  Divide  by  55,  giving  the  quotient  to  the  nearest 
thousandth : 

a  70,034       b  62,158       c  51,329       d  47,676       e  32,983 

10.  Divide   (a)   43,816  by  25.      (b)  3619.4  by  33% 
(c)  260.78  by  12%.     (d)  16.547  by  16%.     Give  quotients 
as  mixed  decimals. 


METHOD 

(a)    25)  43,816  (6)  33%)3619.4 

100)1752.64    Ans.  100)144.77/6  Ans. 

(c)  12^)260.78  (d)  16%)  16.547 

100)16.86/24  Ans.  100). 99/282  Ans. 

Multiply  divisor  and  dividend  by  4  in  (a),  by  3  in 
(6),  by  8  in  (c),  and  by  6  in  (d).  Divide  by  100  by 
shifting  the  decimal  point  in  each  new  dividend  two 
places  to  the  left. 


11.  Divide  by  25.  Write  answers  from  the  book: 
a  164.5     b  321.25  c  2408     d  12.34     e  3750    /  477.5 

12.  Divide  by  16%.  Write  answers  from  the  book: 
a  123.5     b  506.75  c  4802     d  40.25     e  7250     /  307.5 

13.  Divide  by  33%.  Write  answers  from  the  book: 
a  106.4     b  312.25  c  3504     d  20.44     e  4360    /  206.5 

14.  Divide  by  12%.  Write  answers  from  the  book: 
a  125.5     b  273.25  c  1216     d  30.75     e  2430    /  512.5 


298          WALSH'S  BUSINESS  ARITHMETIC 

15.  How  many  tons  of  armor  plate  can  be  bought 
for  $55,440  when  the  price  is  (a)  $175  a  ton?  (b) 
$225  a  ton?  (c)  $275  a  ton? 


METHOD 

(a)  175)  55,440  Multiply    the    divisor 

700)221,760  and  the   dividend  by  4. 

^ns  ~~  cp  \  Give    the    result    as    a 

mixed  decimal. 

Test  the  result  by  multiplying  it  by  175,  using 
the  aliquot  part  method. 


16.  Divide  by  175: 

a  78,995       b  86,387      c  97,244      d  67,011       e  59,822 

17.  Divide  by  225: 

a  39,798       b  28,368       c  48,438       d  79,326       e  65,286 

18.  Divide  by  275: 

a  93,071       b  85,679      c  54,670      d  43,692      e  74,283 

19.  How  many  acres  of  land  can  be  bought   for 
$21,000  when  the  rate  is  (a)  $37^  an  acre?     (b)  $62% 
an  acre?     (c)  $87%  an  acre? 


METHOD 

a  37K)  21,000  Multiply     the    divisor 

300)168,000  and  the  dividend  by  8. 

Ans.  (A.) 


NUMBERS  AND  PROCESSES  299 

20.  Divide  by  37%: 

a  24,000      6  31,500      c  42,360      d  54,813      e  62,172 

21.  Divide  by  66%  (multiply  both  terms  by  3) : 

a  84,000       b  73,200       c  96,480       d  86,214       e  71,203 

22.  Divide  by  62%: 

a  63,000       6  50,500       c  43,280       d  32,105       e  23,456 

23.  Divide  by  75  (multiply  both  terms  by  4) : 

a  18,000       6  23,400       c  36,070       d  42,315       e  50,306 

24.  Divide  by  87%: 

a  63,000       6  75,600       c  89,530       d  97,293       e  86,436 

25.  Divide  by  112%: 

a  72,000       b  60,300       c  53,820       d  53,065       e  32,148 

26.  Divide  by  125.     Give  the  quotient  as  a  mixed 
decimal.     Write    answers    directly    from    the    book. 
(Multiply  both  terms  by  8.) 

a  14,723       b  2345.6      c  325.19       d  40.876      e  .51,234 

27.  Divide  by  375: 

a  63,273       b  76,543       c  81,951       d  93,252       e  87,345 

28.  Divide  by  625.     Try  to  write  answers  from  the 
book  by  multiplying  both  terms  by  16: 

a  43,210       b  32,104       c  21,043       d  10,234       e  54,321 

29.  Divide  by  875: 

a  30,387   6  26,614   c  43,638   d  60,501   e  10,605 


300         WALSH'S  BUSINESS  ARITHMETIC 

30.  Divide  by  133%: 

a  12,345       6  23,456       c  34,567       d  45,678       e  56,789 

31.  Divide  by  166%.     Write  answers  from  the  book. 
(Multiply  both  terms  by  6.) 

a  63,421       b  70,416       c  86,235       d  91,314       e  82,031 

DECIMAL  DIVISORS 
WRITTEN  EXERCISES 

1.  (a)  A  man  pays  annually  as  interest  .06  of  the 
sum  he  borrowed  to  help  to  pay  for  a  house.  If  the 
interest  is  $135  a  year,  how  much  did  he  borrow? 

(b)  Divide  8.36  by  1.6 


METHOD 

(a)  /06) $135/00  Multiply    the     divisor    by 

Ans.  $2250  100  by  canceling  the  decimal 

point.       Multiply    the    divi- 
dend by  100  by  annexing  two  ciphers. 

Divide  the  new  dividend  by  the  new  divisor. 
(6)  Multiply  the  divisor  by  10  by  canceling  the 
decimal  point.    Multiply  the  divi-  (ft)       } 

dend  by  10  by  shifting  the  decimal  

point  one  place  to  the  left,  cancel- 
ing the  original  one. 


(a)  To  show  the  change  in  the  dividend,  place  a 
decimal  point  after  5.  Cancel  it  when  annexing  the 
ciphers. 


NUMBERS  AND  PROCESSES  301 

2.   Find  quotients: 
a  1.5)2.97         b  .16)18  c  .08)322  d  .007). 1001 

e  .4)2.762        /  .09)538.2         g  1.1)16.016         h  .12)836.1 

SIGHT  EXERCISES 

When  the  decimal  divisor  is  an  aliquot  part  of  1, 
that  is,  when  it  equals  &  %,  %,  X6,  change  it  to  the 
equivalent  fraction. 

1.  Give  answers: 

a  3.1  +  .5         b  62  +  .25         c  .81  4-  .125         d  2.2  4-  .0625 

2.  Divide: 

a  3.2  -i-  .4       b  21  -=-  .375       c  3.5  -v-  .625       d  .21  ~  .875 

WRITTEN  EXERCISES 

Change  each  of  the  following  divisors  to  a  whole 
number  by  multiplying  it  by  2,  4,  or  8. 

1.  Find  quotients.     Write  answers  from  the  book: 
a  63.4  -h  .25       b  216  -s-  2.5       c  9.03  -=-  1.25       (2  876  -^  .125 

2.  Divide: 

a  63.5  -  .375     6  495  -  .625     c  8.03  -  .875     d  8.03  ^-  6.25 
e  4.96  -v-  12.5    /  333  -  3.75     g  4.05  -r-  62.5     h  119  4-  875 

DIVIDING  BY  99 

A  computer  would  not  use  long  division  in  dividing 
by  99  or  999. 

PREPARATORY  EXERCISES 

1.    Give  quotients  and  remainders: 
a  99)100       b  99)200       c  99)300       d  99)500       e  99)800 


302         WALSH'S  BUSINESS  ARITHMETIC 

How  does  each  quotient  compare  with  each  re- 
mainder? 

2.  In  dividing  (a)  103,  (6)  305,  (c)  509,  (d)  713,  (e) 
937,  by  99  how  much  more  than  3  is  the  remainder 
in  (a)?     Than  5  is  the  remainder  in  (&)?     Than  9  is 
the  remainder  in  (c)?     Than  13  is  the  remainder  in 
(d)  ?     Than  37  is  the  remainder  in  (e)  ? 

3.  In  dividing  12  hundred  by  99,  what  is  (a)  the 
quotient?     (6)  The  remainder? 

4.  In  dividing  24  hundred  72    (2472)   by   99,    (a) 
What  is  the  quotient?     (6)  How  much  more  than  72 
is  the  remainder?     (c)  \Vhat  is  the  remainder? 

To  divide  a  three-  or  a  four-place  number  by  99,  cut 
off  the  two  right-hand  figures  (tens  and  ones).  The 
remaining  figures  give  the  quotient;  to  obtain  the 
remainder  add  the  quotient  figures  to  those  cut  off. 

SIGHT  EXERCISES 

1.  (a)  At  99  cents  each,  now  many  baseballs  can 
be  bought  for  $12.75,  and  how  much  will  remain? 
(6)  Divide  2445  by  99. 


METHOD 

(a)  1275ff -f- 99^  =  12   (baseballs);    remainder  87  £ 

(lit  +  750 
(6)  2445  +  99  =  24;  remainder  69  (24  +  45) 


2.   Divide  by  99.     Give  quotients  and  remainders: 
a  1841      6  2306      c  3560      d  4324       e  5009      /  6213 


NUMBERS  AND  PROCESSES  303 

3.  Divide  by  99  (a)  8514;    (b)  7230. 

In  (a)  the  quotient,  according  to  the  foregoing  rule, 
is  85  and  the  remainder  is  99;  the  correct  quotient  is, 
therefore,  86. 

In  (b)  the  remainder  102  indicates  that  the  number 
72  should  be  increased  by  1,  making  the  quotient  73; 
the  remainder  is  3  (102-99). 

4.  Divide  by  99.     Give  quotients  and  remainders: 

a  2080      b  3090      c  4060       d  2182      e  3180     /  4260 

These  examples  are  given  to  show  pupils  that  such 
a  divisor  as  99,  which  seems  a  difficult  one  to  them,  is 
really  a  very  simple  one  to  computers;  999  is  a  still 
easier  divisor. 

A  similar  method  is  used  in  dividing  by  98  and  998; 
also  by  89,  79,  69,  etc. 

LONG  DIVISION 
SIGHT  DRILLS 

The  guesses  made  by  some  pupils  to  obtain  the 
successive  quotient  figures  in  a  long  division  example 
show  their  need  of  sight  drills  similar  to  those  given 
below : 

1.   Find  quotients: 

a  20)140  b  30)270  c  40)160  d  50)250 

e  60)420  /  70)210  g  80)480  h  90)360 

i  80)560  j  70)490  k  60)360  I    50)450 


304          WALSH'S  BUSINESS  ARITHMETIC 

Obtain  the  quotient  of  each  of  the  foregoing  by 
dividing  14  by  2,  27  by  3,  etc.,  rejecting  the  cipher  in 
each  term. 

In  the  next  set,  think  of  19,  29,  etc.,  as  less  than  20, 
30,  etc.  Since  20  is  contained  9  times  in  180,  19 
must  be  contained  9  times  with  a  remainder. 

2.  Give  quotients,  omitting  remainders: 

a  19)140  b  29)270  c  39)160  d  49)250 

e  59)420  /  69)210  g  79)480  h  89)360 

i   79)560  j  69)490  k  59)360  I   49)450 

Since  7  times  20  is  140,  7  times  21  is  more  than  140; 
the  latter,  therefore,  will  contain  21  only  6  times  with 
a  remainder.  In  giving  the  quotient,  say  6,  omitting 
the  remainder. 

3.  Give  quotients.     Omit  remainders: 

a  21)140  b  31)270  c  41)160  d  51)250 

e  61)420  /  71)210  g  81)480  h  91)360 

i  81)560  j  71)490  k  61)360  I   51)450 

4.  Omit  a  remainder  when  there  is  one: 

a    210)840         b  430)860         c    310)930         d  510)8570 

e    209)840        /  429)860         g   309)930         h  509)3570 
i    211)840        j   431)860         k  311)930         I    511)3570 


NUMBERS  AND   PROCESSES  305 

m  150)750         n  199)800         o   209)680         p  499)2510 

q    149)900         r   202)800         s    129)390         t    391)2420 
u    151)600         v   296)900         w  131)390         .T  411)3690 

Before  a  set  of  long  division  examples  is  worked, 
these  should  be  used  as  drills,  in  which  successive 
pupils  are  asked  to  announce  rapidly  the  first  quotient 
figure  of  each. 

MULTIPLYING  AND   SUBTRACTING 

PREPARATORY  EXERCISES 
345 

1.   Express  -—  as  a  mixed  number. 


METHOD 

First  write  7  as  the  integral  part  of  the  quotient 
~  _  and  47  as  the  denominator  of  the  frac- 

=  7  —  tion.     Obtain  the  figures  of  the  numer- 

47  ator  thus: 

Think  49  (7  times  7)  and  6  (writing  6)  are  55. 
Think  28  (7  times  4),  33  (carrying  5)  and  1  (writ- 
ing 1)  are  34.     Ans.  7% 


2.    Give  quotient  as  mixed  number.     Write  answers 
from  the  book. 

a  iff.       b  w       e  e^       d 

a  W      h^f-      i  ^      j 


306         WALSH'S  BUSINESS  ARITHMETIC 

WRITTEN  EXERCISES 

1.  At  59  tons  to  the  car,  how  many  car  loads  are 
there  in  43,567  tons,  and  how  many  tons  are  there 
over? 


ONE  WAY 

Ans.    738  (C.  L.);  remainder  25  T. 
59  T.)43567  T. 
413 
226 
177 


497 

472 


In  long  division  write  the  quotient  above  the 
dividend.  The  first  partial  dividend  is  435.  Ob- 
tain 7,  the  first  quotient  figure,  by  dividing  43  by 
6  (the  divisor  being  nearly  60).  Write  7  above  5, 
the  last  figure  of  the  partial  dividend. 

After  738,  the  quotient,  write  C.  L.  (car  load) 
in  a  parenthesis,  followed  by  the  remainder,  25  T. 


Thousands  of  European  children  are  taught  only 
the  following  method  in  long  division.  Surely  Ameri- 
can boys  and  girls  should  be  willing  to  use  it  if  time 
can  thus  be  saved.  The  greater  concentration  re- 
quired tends  to  secure  accuracy. 

2.   Divide  417,739  by  59. 


NUMBERS  AND  PROCESSES  307 


ABBREVIATED    FORM 

Ans.    7080;  remainder  19.        This    method    con- 

59)417739  sists  in  multiplying  and 

473  subtracting      in      one 

19  operation,  omitting  the 

partial  products. 

Having  written  7,  the  first  quotient  figure,  think 
63  (7  times  9)  and  4  (writing  4)  are  67;  think  35 
(7  times  5),  41  carrying  6.  This  being  the  same 
as  the  remaining  figures  of  the  partial  dividend, 
the  remainder  is  4. 

To  4,  the  remainder,  annex  7,  the  next  figure  of 
the  dividend,  making  47  the  next  partial  dividend. 

Since  47  does  not  contain  59,  write  a  cipher  in 
the  quotient  and  bring  down  3,  the  next  figure 
of  the  dividend,  making  473,  the  next  partial 
dividend. 

Write  8,  the  next  quotient  figure,  and  think  72 
(8  times  9),  and  1  (writing  1)  are  73;  think  40  (8 
times  5),  47  (carrying  7). 

To  1,  the  remainder,  annex  9,  making  19  the  next 
partial  dividend. 

Since  19  does  not  contain  59,  write  a  cipher  in 
the  quotient. 

Be  careful  to  locate  properly  the  first  quotient 
figure,  and  to  write  a  figure  (which  may  be  a  cipher) 
over  each  of  the  remaining  figures  of  the  dividend. 
Before  making  one  of  the  tests  specified  below,  note 
that  the  quotient  has  the  required  number  of  figures. 


308          WALSH'S  BUSINESS  ARITHMETIC 

Test  the  foregoing  result  by  multiplying  7080  (the 
quotient)  by  59  (the  divisor)  and  adding  to  the  product 
19  (the  remainder). 

Or  by  casting  out  ll's,  multiply  7  (the  quotient 
excess)  by  4  (the  divisor  excess).  To  this  product, 
add  8  (the  remainder  excess),  which  gives  3  as  the 
excess.  The  dividend  excess  is  3,  which  agrees  with 
the  other  result. 

SIGHT  DRILLS 

Before  taking  up  the  following  examples  there  should 
be  a  rapid  drill  in  giving  the  first  quotient  figure  of 
each  example  and  the  number  of  figures  in  the  quo- 
tient. 

WRITTEN  EXERCISES 

1.  Divide,  using  either  the  abbreviated  form  or  the 
longer  one.     Test  each  result: 

a  4000  -7-41  b    13,582  +  501  c  908,671  +  1023 

d  5871  +  61  e    26,154  +  702  /  777,349  -  2056 

g  6325  +  71  h   70,000  +  803  i  470,493  +  3142 

;  7320  +  81  k  52,610  +  423  /  839,264  +  4026 

m  9065  H-  51  n  46,792  +  315  o  678,579  +  3205 

p  5216  +  91  q   63,130  +  269  r  708,000  +  1684 

s  9653  +  31  t    83,746  -  137  u  853,568  +  2245 

v  6885  +  21  w  94,217  +  621  x  956,308  +  3189 

2.  At  a  railroad  terminal  794  car  loads  of  freight 
were  received,  weighing  63,018  tons.     What  was  the 
average  load  per  car?     Give  answer  (a)  to  the  nearest 
hundredth,     (b)  To   the   nearest   tenth,     (c)  To   the 
nearest  integer. 

Test  each  result. 


NUMBERS  AND  PROCESSES  309 


PROCESS 

79.367  (a)  79.37  T.  Ans. 


794)63018. 

7338  (6)  79.4    T. 

2920 

5380  (c)  79  T. 

6160 

Test  (a)  by  adding  616  to  the  product  of  7936  and 
794.  Test  (b)  by  adding  538  to  the  product  of  793 
and  794.  Test  (c)  by  adding  292  to  the  product  of 
79  and  794. 

In  giving  the  answer  to  (a)  write  7  as  the  fourth 
figure  of  the  quotient,  since  7,  the  next  figure,  is 
greater  than  5.  In  giving  the  answer  to  (b)  write  4 
as  the  third  quotient  figure,  since  6,  the  fourth 
figure,  is  greater  than  5.  In  giving  the  answer  to 
(c)  write  79,  the  next  figure  being  less  than  5. 


3.  Divide.     Give  each  answer  to  the  nearest  integer: 
a  4000  -i-  43         b  23,582  -^  431         c  129,456  -i-  531 

4.  Divide.     Give  answers  to  the  nearest  tenth: 

a  5871  -  51         6  36154  ^  732          c  248,673  -*•  727 

5.  Divide.     Give  answers  to  the  nearest  hundredth: 
a  6325  +  81         b  47,000  -*-  723         c  320,000  -5-  337 

d  7974  -i-91         e  52,318  -  864        /  562,873  -5-  739 

6.  (a)  How  many  kilos  of  2.2046  pounds  each  are 
equivalent   to   54.75    pounds?     (b)  What   decimal   of 
a  meter,  39.37  inches,  is  a  yard? 


310          WALSH'S  BUSINESS  ARITHMETIC 


PROCESS 

Ans.     24.834  (kilos)     Multiply  the  divi- 
(a)  2/2046.)54  /7500.  sor    by    10,000    by 

10  6580  shifting  the  decimal 

1  83960  point  4  places  to  the 

75920  right.     Do  the  same 

97820  with    the   dividend, 

9636  annexing     two     ci- 

phers.      Carry    the 
result  to  three  decimal  places. 
(b)  Write  the  dividend  as  36  inches,  to  give  it  the 

same  denomination  as  the 
divisor.     Give  the  result  to 
39/37.)36/00.0  the  nearest  thousandth. 


7.  Give  quotients  to  nearest  thousandth: 

a  38.765  -*-  3.9  b  18,612  -  .095  c  844.73  +  .77 

d  6.5772  -T-  .85  e  511.347  -  .67          /  105.28  4-  5.9 

g  58.6  -5-  .049  h  2406  -.  .43  i  53.95  ^  .083 

8.  Divide    292.2331903    by    46.72352,    giving    the 
result  correct  to  thousandths. 


46.724)292.233 

9.   Give  quotients  correct  to  thousandths: 

a  18.54875  -*-  3.23852  b  76.824  -:-  .74325 

c     8.32346  -5-  .72149  d  1634.7853  -r-  22.37425 

e     .093285  +  .005873  /  398.647  +  93.0286 

g  .0065437  +  .85436  h  73.0248  +  1.63387 


NUMBERS  AND  PROCESSES  311 

MULTIPLYING  AND  DIVIDING 

CANCELLATION 
PREPARATORY  EXERCISES 

1.  (a)  At  $16  a  week  of  44  hours,  what  is  the  pay 
of  a  girl  who  works  33  hours?  (b)  What  wages  does  a 
boy  receive  for  39  hours'  work  at  the  rate  of  $18  a 
week  of  54  hours? 


METHOD 

In  (a)  multiply  the  weekly  rate,  $16,  by  %,  the 
fraction  of  the  week  she  works. 

In  (b)  multiply  the  hourly  rate,  $%  by  39,  the 
number  of  hours  she  works. 


2.  (a)  What  is  the  value  of  321  eggs  when  they  are 
worth  36  cents  a  dozen?     (b)  Of  360  eggs  at  the  rate 
of  43  cents  a  dozen? 

3.  Give  the  cost  (a)  of  131  pounds  of  potatoes  at 
$1.80  a  bushel  of  60  pounds,     (b)  Of  120  pounds  at 
$1.70  a  bushel. 

4.  Give  answers : 


a  16  xff 
e  W  X  131 
.  246  X  72 

b  |f  X39 
/  170  X  J^ 
.  123  X  93 

c  321  X  ff 
9  HX60 
,  130  X  42 

d  spf.  x  43 
h  84  x  W 
24  X  125 

82 
82  X  72 

J   279 
123  X  279 

65 

65x42 

120 
120  X  125 

24 


312          WALSH'S  BUSINESS  ARITHMETIC 

WRITTEN  EXERCISES 

1.  Find  the  cost  of  a  rectangular  plot  154  yards 
long  68  yards  wide  at  the  rate  of  $275  an  acre  (4840 
sq.  yd.)- 


ONE  WAY 

First  find  the  number  of  square  yards  by  multi- 
plying 154  by  68,  which  gives  10472.  Divide  this 
by  4840  to  ascertain  the  number  of  acres  (2%$  A.). 
Multiply  $275  by  2%*. 

A   BETTER   WAY 

154  X  68  X  $275          Indicate  the  area  in  square 

4840  yards     by     writing     154  X  68. 

Draw  a  line  and  indicate  the 

number  of  acres  by  writing  4840  underneath  (as  a 

divisor).     Indicate  that  this  result  is  to  be  used 

to   multiply  $275,  by  writing  after  it    the    latter 

preceded  by  a  multiplication  sign.     Cancel. 


In  computations  involving  only  multiplication  and 
division,  indicate  the  operations,  then  shorten  the 
work  by  cancellation. 

2.  Find  answers: 

12  X  7  X  153     85  X  126  X  13     454  X  198  X  72 
19  X  49         17  X  91        81  X  63  X  35 

3.  Find  the  value  of: 

484  X  .06  X  210       24.5  X  18.7 
a  '     360  .238 


NUMBERS   AND   PROCESSES  313 


PROCESS 

.01 

a  484  X  .06  X  210  In  canceling  .06  and  36  by  6, 

3()()  ke  careful  to  write  .01  above 

g  the  former. 

b  Since  the  divisor  .238  contains       24/5  X  18/70 
three  decimal  places,  annex  a 
terminal  decimal  cipher  to  one 
of  the  numbers  above  the  line,  giving  a  total  of 
three   places   in   the   dividend.     Cancel   all   the 
decimal  points. 

This  multiplies  the  divisor  by  1000,  and  the 
dividend  by  10  and  again  by  100. 


4.   Find  the  value  of  each  of  the  following: 

18.9  X  12  X  49  1.89  X  12  X  4.9  18.9  X  .12  X  .49 

6.3  X  21  2.1  X  .63  .63  X  .21 


DIVISION   OF  FRACTIONS 
PREPARATORY  EXERCISES 

1.  How  many  times  is  2  thirds  contained  in  3  thirds? 
Give  answer  (a)  as  a  mixed  number,  (6)  as  an  improper 
fraction. 

2.  Divide  1  by  %,  giving  quotient  as  an  improper 
fraction. 

3.  If  %  goes  /2  times  into  1,  how  many  times  does  it 
go  (a)  into  5  times  1?     (b)  Into  7  times  1?     (c)  Into 
9  times  1? 


314          WALSH'S  BUSINESS  ARITHMETIC 

4.  Give  quotients: 

a  3  halves)^  halves         b  %)%  c  %)1  d  1)01. 

e  l+%  f  \^%        9  l+%        hl+% 

The  quotient  of  1  divided  by  a  number  is  called  the 
reciprocal  of  a  number. 

5.  Give  the  reciprocal  of  the  following: 

a  1%         b  2        c  %        d%        e  5/5        /  2% 
To  get  the  reciprocal  of  a  common  fraction  invert  its 
terms. 

WRITTEN    EXERCISES 

1.  Find  the  average  yield  per  acre  (a)  when  27 
acres  yield  496%  bushels,  (b)  When  28%  acres  yield 
693  bushels,  (c)  When  36%  acres  yield  790%  bushels. 


(a) 

(D 
496%  •*•  27  = 

PROCESS 
(II)                       (HI) 

Cancel 

/s 

8           1 

8         27 

(b) 

693  -=-  28%  = 

693      231 
T~      ~8~ 

693        8 

i    Ssi 

Cancel 

„       6321       147      6321         4 
(c)  790%  -r-  36%  =  —  -5-  —  =  —JT-  X  —     Cancel 

(I)  shows  each  example  in  the  original  form; 
(II)  shows  the  divisor  and  the  dividends  written 
as  fractions;  (III)  substitutes  for  each  divisor  its 
reciprocal  and  changes  the  sign  of  division  to  that 
of  multiplication. 

TEST 

Multiply  the  result  by  the  divisor. 


NUMBERS  AND  PROCESSES  315 

2.   Find  quotients.     Estimate  the  integral  part  of 
each  result  before  beginning  work: 


a  436  -r-  18% 
d  973  -=-  34% 
g  678  -r-  42% 

j  279  -5-  13% 
m  777  -^  29% 

b  330%  -:-  23 

e  924%  -r-  19 
/i  788%  -  57 
A;  425%  +  16 
n  806%  -  30 

c  907%  -  24% 
/  787%6  -  42% 
i  870%  -  36% 
/  665%  -  16% 
o  231%  -  10% 

p  357  -*-  14%     g  528%  -  21     r  404%  -  13% 
s  825  -;-  31%     /  291%  +  18     u  545%.  -s-  21% 

v  564  -s-  15%     w  607%  -s-  22     a;  374%  -r  18% 

,  8%  X  6%  X  4%  X  1% 
3.  Find  the  value  of  - 

5%  X  3%  X  5%  X  2% 


METHOD 

2%  X  3%  X  %  X  %  X  %6  X  K5  X  &  X  % 

Change  the  mixed  numbers  in  the  compound 
dividend  to  improper  fractions.  Then  write  as 
multipliers  the  reciprocals  of  the  fractions  in  the 
divisor.  Cancel. 


4.   Find  the  value  of: 

6%  X  5%  ,   3%  X  16%  60%  X  3% 

0 


27  X  3%  2%  X  %  14%  X  % 

5.  At  $%  a  yard,  how  many  yards  of  dress  goods 
can  be  bought  for  $127%? 

NOTE:  In  dividing  by  %,  %,  %,  %,  etc.,  business  men  frequently  use  the 
reciprocals  in  their  mixed  number  forms,  viz.,  1&  1%,  1%,  1#,  etc.,  instead 
of  the  respective  improper  fractions:  %,  %,  %,  %,  etc. 


316         WALSH'S  BUSINESS  ARITHMETIC 
6.   Divide  127%  (a)  by  %,  (b)  by  £  (c)  by  %. 


METHOD 

(a)  127%  (-%)  X  IX  (6)  127%  (-s-jflx  IK 

Add%42%  AddK 


_ 

170    Ans.  159%  Ans. 

(c)  127%  (*50X  1% 
AddK    25% 
153 

Inclose  each  divisor  in  a  parenthesis  and  write  its 
reciprocal  as  a  multiplier.  Multiply  127%  by  1%  in 
(a),  by  IK  in  (6),  by  1%  in  (c),  by  adding  to  it  %,  X, 
K,  respectively,  of  itself.  Test  the  result  in  (a)  by 
multiplying  42%  by  4;  in  (6)  by  multiplying  31% 
by  5;  in  (c)  by  multiplying  25%  by  6. 


7.  Find  quotients: 

a  1356%    4-  %  b  6876%  -  %  c  7594%  -  % 

d  2796%    -s-  X  «   7641%  -=-  %  /  6463%  -^  % 

0  3475%    +%  h  8438%  -:-  %  i  5929%  -=-  % 

j  4004  &  4-  %  &  9567%  ^-  %  /   4613%  -j-  % 

m  5256%  •«-  %  n  8360%  +  X  o  3722%  -  % 

p  6234%    +%  q  7642%  +  X  r  2363%  -  % 

s  7042%    ^  %  <    6907%  -s-  X  u  1276%  ^-  Xo 

t;  8629%    -5-  %  w  5005%  +  X  «  2563%  -s-  % 

8.  At  $1%  a  bushel,  how  many  bushels  of  potatoes 
can  be  bought  for  $127%? 

9.  Divide  127%  (a)  by  1%,  (b)  by  IX,  (c)  by  1%.    Test 
each  result. 


NUMBERS  AND  PROCESSES  317 


METHOD 

(a)  127X2  (+  1)0  X  % 


Deduct  X 


85  Ans. 


(6)  I27y2  (-5-  DO  x  % 


Deduct  X    31 


95%  Ans. 

(c)  127%  (•*•  IK)  X  % 
Deduct  X    21X 

106%  Ans. 

Inclose  each  divisor  in  a  parenthesis  and  write 
its  reciprocal  as  a  multiplier. 

Multiply  127M  by  %  in  (a),  by  %  in  (6)  and  by  %  in 
(c),  by  deducting  from  it  %,  %  and  X,  respectively, 
of  itself. 

Test  the  result  in  (a)  by  multiplying  42%  by  2; 
in  (6)  by  multiplying  31%  by  3;  in  (c)  by  multiply- 
ing 21%  by  5. 

10.   Find  quotients: 

a  1353%  -s-  1%  b  5005K  -s-  1%  c  7164%)  •*•  IX 

d  2496%  4-  IK  c  5005M  -s-  W  /  8363%  •*•  1% 

g  3075%  -s-  IK  h  6328%  ^  1^  i  9009%  •*-  iMo 

j  4238){  H-  IX  A;  7593%  -  Itf  /  8657^    4-  IX 


SECTION  IV 

PRODUCTION  AND  CONSUMPTION 
CHAPTER  ONE 

PROBLEMS    OF    THE    CONSUMER 
HOUSEHOLD  EXPENSES 

The  calling  followed  by  the  largest  number  of  per- 
sons is  that  of  home  keeping.  Success  in  this  line, 
as  in  any  other,  requires  the  employment  of  business 
methods.  Efficient  management  is  just  as  important 
in  spending  the  income  as  it  is  in  earning  it. 

FAMILY  BUDGETS 

The  following  table  shows  the  average  outlay  of  a 
large  number  of  families  in  various  sections  of  the 
United  States  for  food,  for  shelter,  and  for  clothing, 
arranged  by  classes  having  incomes  as  specified. 


Expenditures  for 

Remainder  for 

Yearly 

operating  ex- 

Income 

Food 

Shelter 

Clothing 

penses,  savings, 
etc. 

$(500 

$258 

$114 

$78 

(a) 

900 

378 

162 

126 

(6) 

1200 

444 

204 

180 

W 

1500 

510 

255    * 

270 

(d) 

318 


PRODUCTION  AND  CONSUMPTION        319 


WRITTEN  EXERCISES 

1.  Write  from  the  book  the  sum  represented  by 
(a),  by   (6),  by   (c)  and  by   (d),  respectively,  in  the 
foregoing  table. 

2.  Make  out  a  table  similar  in  form  to  the  fore- 
going, but  changing  the  money  to  per  cents  in  the  last 
four  columns. 

3.  Before  the  war  the  following  was  Mrs.  Kirby's 
estimate  of  the  minimum  food  requirements  of  Mr. 
Kirby  and  herself,  and  their  three  children. 


Meats,  etc. 
5  Ib.  beef 

l/2     "       "    (stew) 
%     "  pork 
Y2     "  ham 
1     "  chicken 
1%  "  fish 


"  36^ 
"  18^ 
"  12f5 


Milk,  Eggs,  etc. 

1  Ib.  butter 

/2  4<  cheese  "  20^ 

2  doz.  eggs  "  32^ 
16  qt.  milk                "    6^ 


Cereals,  etc. 
21  loaves  bread         @    5ff 

1  doz.  rolls  "  10^ 

2  Ib.  cake  "  10£ 

%    "  rice  "     8^ 

2     "  flour  " 

Z%  "  oatmeal  " 


Sugar,  Tea,  etc. 

1  Ib.  coffee  @ 

2  "  sugar  " 
%  pt.  sirup                  " 
%  Ib.  tea  " 


%  pk.  potatoes 
Turnips  or  carrots 
2  Ib.  onions 
Other  vegetables 
Beans  and  peas 


Vegetables,  etc. 
@  64^  1  can  tomatoes 

5^  ^   '      corn 

"     3^  Fruit 

"  66^  %  Ib.  prunes 

"     5ff  Pickles,  spices,  etc. 


@  20^ 


4.   Find   the   weekly   cost    (a)    of   the  meats,   etc., 
(6)  of  the  cereals,   etc.,    (c)  of   the  milk,   eggs,  etc., 


320 


WALSH'S  BUSINESS  ARITHMETIC 


(d)  of  the  sugar,  tea,  etc.,  (e)  of  the  vegetables,  etc. 
(/)  Find  the  total  weekly  cost,  (g)  Find  the  cost  for 
52^  weeks. 

5.  How  much  did  the  yearly  cost  exceed  42%  of 
Mr.  Kirby's  pay  for  300  working  days  at  $3  a  day? 

6.  The  following  was  the  estimated  cost  of  clothing. 
Mrs.  Kirby's  hats  and  coats,  and  Mr.  Kirby's  over- 
coat were  supposed  to  last  two  years,  one  half  the 
given  price  being  allowed  for  one  year.     The  prices 
were  taken  from  a  schedule  issued  before  the  war. 


Mother's  Clothing 

Father's  Clothing 

2  hats  00                @  $3.— 

1  cap 

@  $0.25 

1  coat  (J0 

8.— 

1  hat 

"       .75 

Isuit 

8.  — 

1  suit 

"  10.— 

3  waists 

.66% 

1  overcoat  00 

"  10  — 

2  dresses 

1.25 

1  pr.  trousers 

"     2.— 

2  petticoats 

.50 

3  shirts 

* 

1.50 

3  aprons 

.15 

2  shirts 

i 

1  — 

6  handkerchiefs 

.07/2 

6  collars 

' 

.10 

6  prs.  stockings 

.10 

2  pr.  overalls 

* 

.75 

2  pr.  shoes 

2.— 

4  ties 

* 

.12)* 

Repairing  shoes 

1.— 

4  handkerchiefs 

* 

.05 

3  suits  underwear     * 

.20 

6  pr.  socks 

* 

.10 

P             «                       M                  4 

.70 

Gloves  and  mittens 

* 

.50 

Linen 

6.— 

2  pr.  shoes 

i 

2.— 

Rubbers 

.50 

Repairing 

i 

1.50 

Sundries                   *     3.— 

2  suits  underwear 

.50 

o      "                  " 

"      .75 

7.  Find  the  annual  cost  of  (a)  the  mother's  clothing. 
(6)  That  of  the  father. 

(c)  Find  the  total  cost  of  the  family  clothing,  in- 
cluding $23.35  for  that  of  the  girl  and  $16.30  for  each 
of  the  two  boys. 


PRODUCTION  AND  CONSUMPTION         321 

(d)  How  much  more  did  the  clothing  cost  than 
14%  of  $900?  (e)  What  should  have  been  the  an- 
nual income,  in  order  that  14%  of  it  would  purchase 
the  specified  clothing  at  the  prices  given? 

8.  The  following  are  estimates  of  the  other  expenses 
for  a  year: 


Rent  $156. —  Recreation 

Car  fare  31.20  Church  dues  10.— 

Fuel  and  light  52.—  Utensils  15.— 

Furniture  52. —  Spending  money 

Insurance  52. —                              (father)  5. — 

Reading  matter  5. —  Sundries  5. — 

a  What  is  the  total  of  the  foregoing  items? 
b  What  was  the  total  amount  of  the  year's  expen- 
ditures including  those  for  food  and  clothing? 

9.  If  Mr.  Kirby's    earnings  of  $900   were  supple- 
mented by  a  year's  interest  at  4  %  on  $1000  he  has  in 
the  savings  bank,  how  much  of  his  income  should 
remain  at  the  end  of  the  year? 

Finding  that  a  house  in  the  suburbs  with  a  piece  of 
ground  could  be  bought  for  a  cash  payment  of  $600 
and  monthly  instalments  of  $15  each  until  the  re- 
mainder, $1200,  was  paid,  with  interest  at  6%,  Mr. 
Kirby  bought  it,  taking  possession  February  1. 

10.  Make  out  a  statement  of  the  first  year's  pay- 
ments, showing  (a)  the  principal  at  the  beginning  of 
each  month;   (b)  the  interest  for  the  month;   (c)  the 
amount  due,  including  interest,  etc.;  (d)  the  payment 
made;  (e)  the  balance  remaining.  (/)  How  much  did  his 
payments  for  the  year  exceed  the  total  of  the  interest  ? 


WALSH'S  BUSINESS  ARITHMETIC 


Date 

Principal 

Interest 
to  date 

Amount 
at  date 

Payment 

Bal. 

Mar.  1 

$1200.— 

$6.— 

$1206.— 

$15 

$1191.— 

Apr.   1 
May  1 

1191.— 
1181.96 

5.96 
5.91 

1196.96 
1187.87 

15 
etc. 

1181.96 
etc. 

etc. 

etc. 

etc. 

etc. 

etc. 

etc. 

NOTE:  Use  no  side  calculations.  The  monthly  interest  is  %%  of  the 
principal.  Do  not  give  fractions  of  a  cent  in  stating  the  interest;  write 
$5.96  for  $5.95&  $5.91  for  $5.9098,  etc. 

11.  (a)  How  much  did  his  interest  payments  amount 
to  for  the  first  year? 

For  purposes  of  taxation,  his  property  was  assessed 
at  $1400,  on  which  he  paid  a  tax  of  %%.  (b)  What 
were  his  taxes  for  the  year?  He  insured  his  house 
for  $1500  at  44  cents  per  $100  for  three  years. 
(c)  What  was  the  cost  of  the  three  years'  insurance? 
He  made  most  of  his  repairs  himself  with  the  help 
of  his  boys,  paying  $15  for  material,  and  only  $7  for 
outside  help,  (d)  How  much  did  he  pay  for  interest, 
taxes,  one  year's  insurance,  and  repairs?  (e)  How 
much  less  did  these  amount  to  than  the  yearly  rent  of 
his  former  residence?  (/)  What  per  cent  of  $1800,  the 
cost  of  the  house,  was  its  assessed  value  of  $1400  ?  (g) 
For  what  per  cent  of  its  cost  was  it  insured? 

12.  How  much  did  he  reduce  his  mortgage  of  $1200 
by  the  end  of  the  year? 

As  soon  as  they  were  settled  in  the  new  house, 
Mr.  Kirby  with  the  help  of  the  boys  fenced  off  a 
portion  of  the  land  for  chickens,  and  bought  materials 
for  a  henhouse  as  follows: 


PRODUCTION  AND  CONSUMPTION         323 

a  226  bd.  ft.  scantling 

b  850    "     "lumber 

c  622    "     "boards 

d  2  pr.  hinges 

e  150  sq.  ft.  roofing  paper 

/  5  Ib.  nails 

g  56  sq.  ft.  poultry  wire 

13.  Find  the  cost  of  each  of  the,  foregoing  items  at 
$32  per  M  (1000  board  feet)  for  the  scantling,  $30  per 
M  for  the  lumber,  $36  per  M  for  the  boards,  50 £  per 
pair  for  the  hinges,  2K^  per  square  foot  for  the  roofing 
paper,  6^  per  pound  for  the  nails,  and  \%i  per  square 
foot  for  the  wire. 

14.  He   bought   23   hens   from   a   neighbor   at   75 
cents  each,      (a)  Find  the  cost  of  the  hens.     The  fol- 
lowing is  the  egg-production  of  a  year,  with  the  aver- 
age price  prevailing  during  the  month: 


Month 

Eggs 
Laid 

Value 
per  doz. 

Month 

Eggs 
laid 

Value 
per  doz. 

Feb. 
Mar. 
Apr. 
May 
Jun. 
Jul. 

330 
461 
393 
358 
357 
344 

40^ 
36 
32 
30 
32 
33 

Aug. 
Sep. 
Oct. 
Nov. 
Dec. 
Jan. 

334 
129 
99 
104 
153 
254 

34£ 
36 
40 
42 
44 
42 

(6)  Find  the  number  of  eggs  laid  during  the  year, 
(c)  their  value,  (d)  the  average  value  per  dozen. 

15.  During  the  year  the  garden  patch  yielded  the 
following : 


324          WALSH'S  BUSINESS  ARITHMETIC 

15    quarts  of  string  beans         2  bushels  of  turnips 
2K  "lima  12  "tomatoes 

2K  "  navy  100  heads      "  cabbage 

3  bushels  of  beets  20  bunches  "  carrots 

2  "onions  150  "radishes 

3  '  peas  10  dozen  cucumbers 
IK       "      "  spinach 

Find  the  value  of  the  foregoing  at  the  prices  pre- 
vailing in  the  vicinity  of  the  school. 

16.  Mr.  Kirby's  payments  for  food  were  reduced 
$2.80  a  week,  owing  to  the  home  production  of  eggs 
and  vegetables,  the  daily  surplus  being  preserved  for 
winter  consumption.  Find  the  saving  of  52%  weeks. 

"BALANCED"  MEALS 

A  day's  meals  should  supply,  in  proper  quantities, 
protein,  carbohydrates,  fats,  mineral  matter,  water. 

Protein  supplies  the  tissue  building  materials,  to- 
gether with  some  of  the  heat  and  energy.  It  is  chiefly 
obtained  from  the  whites  of  eggs,  lean  meat,  skimmed 
milk,  gluten  of  wheat,  etc. 

The  best  known  of  the  carbohydrates  are  the  sugar 
and  the  starch  of  foods.  These  yield  energy  in  the 
form  of  heat  and  the  power  to  do  work. 

Fat  is  obtained  from  cereals,  eggs,  nuts,  cream,  etc. 
It  yields  a  larger  amount  of  energy  according  to  its 
weight  than  does  either  of  the  other  two  groups. 

Mineral  matter  comes  from  green  vegetables,  fruits, 
cereals,  and  milk. 


PRODUCTION  AND  CONSUMPTION 


325 


The  day's  meals  of  a  mechanic  should  provide  about 
4  ounces  of  protein  and  3500  calories  of  energy. 

The  following  are  the  meals  of  a  man  doing  clerical 
work: 


Kind  of  Food 


Weight      Cost         Protein          Energy 


Breakfast 

Cereal    Hominy 

2  oz. 

%>£ 

.166oz. 

206  calories 

Meat      Sausage  cakes 

3 

3% 

.390   " 

398 

Bread    f  Toast, 

3 

1 

.273   " 

210 

Butter  \  %  cu.  in. 

X 

IX 

— 

112 

Beverage  |  g  °g^e 

X 

ft 

— 

57 

Fruit      Prunes 

2 

1 

.042   " 

175 

Total  for  meal 

(a) 

(6) 

(c) 

GO 

Dinner 

Meat           Beef  stew 

8    oz. 

3%^ 

.449  oz. 

330  calories 

Vegetable    Rice 

2    •" 

1M 

.160   " 

324 

"         Green     Spinach 

2     " 

IK 

.042   " 

32 

Dessert  (  Cherry  roll 

5K  " 

2% 

.217   " 

353 

\  Sauce 

\%  " 

1% 

— 

225 

Bread    (  2  slices 

2     " 

% 

.182   " 

140 

Butter  \  %  cu.  in. 

X  " 

IX 

— 

112 

Total  for  meal 

W 

(/) 

(9} 

(h) 

Supper 

Animal  food     Cottage  cheese 

5    oz. 

1%^ 

1.145oz. 

160  calories 

Vegetable          Potato  cakes 

4      " 

1 

.088   " 

96       " 

Bread    f  3  slices 

3      " 

1 

.273   " 

210       " 

Butter  \  %  cu.  in. 

%  " 

1% 

— 

140       " 

Beverage    Cocoa 

5%   " 

1% 

.216   " 

193 

Total  for  meal 

(0 

0') 

(*) 

(0 

Total  for  day 

(») 

(n) 

(o) 

w 

WRITTEN  EXERCISES 


1.   Find  the  weight  of  the  food  for  each  meal,  (a), 
(e),  and  (i);  the  total  for  the  day  (m);    the  cost  for 


326 


WALSH'S  BUSINESS  ARITHMETIC 


each  meal  (6),  (/),  and  (j);  the  total  cost  for  the  day 
(n);  the  quantity  of  protein  for  each  meal,  (c),  (g),  and 
(fc);  the  total  for  the  day  (o);  the  amount  of  energy 
supplied  by  each  meal,  (d),  (h),  and  (/);  the  total  for 
the  day  (p). 

The  following  table  gives  the  most  important  items 
of  one  type  of  a  United  States  soldier's  service  ration 
for  a  day : 


Protein 

Calories 
per  Ib. 

Protein 

Calories 
per  item 

Bacon 

16        oz. 

15% 

2080 

(a) 

0) 

Flour 

18 

11.5% 

1680 

(6) 

& 

Beans 

2.4     ' 

22.5% 

1600 

(c) 

to 

Potatoes 

20 

1.8% 

320 

(d) 

m) 

Prunes 

1.28   ' 

2.1% 

1440 

(0) 

(«•) 

Sugar 

3.2     ' 

— 

1868 

(/) 

(o) 

Milk 

.5     " 

9#% 

784 

(f) 

to 

Lard 

.64   " 

— 

4320 

(h) 

(?) 

Butter 

.5     " 

1% 

3608 

(*) 

w 

Totals 

w 

CO 

2.  From  the  foregoing,  find  the  quantity  of  protein 
in  each  item,   (a)  to   (i);    the  number  of  calories  in 
each,    (j)   to   (r);    the  total  amount  of  protein,    (s); 
and  the  total  number  of  calories,  (/). 

3.  How  many  times  4  ounces  is  (s)? 

4.  How  many  times  3500  calories  is  (<)? 

6.   Find  the  number  of  pounds  of  each  of  the  follow- 
ing required  for  a  detachment  of  6000  men: 


(a)  Bacon 
(6)  Flour 
(c)  Beans 


(d)  Potatoes 

(e)  Prunes 
(/)  Sugar 


(g)  Milk 
(h)  Lard 
(i)  Butter 


PRODUCTION  AND  CONSUMPTION        327 

6.  Find  the  total  quantity  of  food  required  a  day 
for  the  same  detachment,  including  the  following: 

Coffee          420  Ib.        Pepper  60  Ib. 

Vinegar        120  "          Cinnamon  21  " 

Sirup  120  "          Lemon  Extract        21  " 

7.  Find  the  daily  quantity  allowed  to  each  man. 

A  SAMPLE  UNITED  STATES  MENU 

The  cost  to  the  Government  of  the  standard  ration 
is  now  38Kj£  a  day.  For  the  various  specified  items, 
the  use  of  other  articles  is  authorized  when  the  latter 
supply  the  proper  nourishment,  and  the  cost  of  the 
ration  does  not  exceed  the  Government  allowance. 

The  following  table  gives  the  cost  of  a  day's  meal 
to  1700  men  at  a  training  camp: 

BREAKFAST 

Cereal                     Milk  Toast  $19.60 

Meat                       Ham  Omelet  55.60 

Vegetable                 Fried  Potatoes  20.00 

Bread                      Rolls  and  Butter  25.00 

Beverage                  Coffee  and  Milk  36.00 

Total  (a) 

DINNER 

Soup                        Beans  $24.60 

Meat                        Fried  Liver  80.00 

Vegetable                 Baked  Potatoes  36.00 

Fried  Onions  22.80 

Bread                      Bread  16.00 

Dessert                    Coffee  Cake  30.00 

Beverage                 Lemonade  33.00 

Total  ~W~ 


328 


WALSH'S  BUSINESS  ARITHMETIC 


Meat 
Vegetable 
Bread 
Dessert 

Beverage 


SUPPER 

Beef  Roll  $32.00 

Sweet  Potatoes  21.00 

Bread  and  Butter  17.00 

Cake  30.00 

Lemon  Sauce  12.65 

Coffee  with  Milk  20.00 

Total  (c) 

WRITTEN  EXERCISES 

Find  the  cost  of 
each  meal,  (a),  (6), 
and  (c).  Find  (d)  the 
total  cost  for  the  day. 
Find  (e)  the  daily 
cost  per  soldier.  Find 
(f)  the  difference  for 
1700  soldiers  between 
(d)  and  the  Govern- 
ment allowance  of 
a  day. 


SOLDIERS   AT   MESS 


EFFICIENCY  IN  HOME  KEEPING 

No  matter  how  small  the  sum  available  for  food, 
the  efficient  manager  supplies  the  necessary  nourish- 
ment. She  purchases  cheaper  cuts  of  meat,  and  makes 
them  just  as  palatable  as  the  higher-priced  ones. 
By  carefully  watching  the  market  she  is  able  to  give 
her  table  the  needed  variety. 

She  is  careful  to  require  the  butcher  to  give  her  all 


PRODUCTION  AND   CONSUMPTION         329 

the  fat  and  the  bone  that  have  been  weighed  and 
charged  for.  The  water  in  which  vegetables  have  been 
boiled,  and  which  contains  important  mineral  con- 
stituents, she  uses  in  making  soup.  No 'stale  bread 
is  wasted,  being  made  into  tasty  desserts. 


THE   NUMBERS   ON   THIS   PICTURE   LOCATE   VARIOUS   CUTS   OF   BEEF 


High  Cost  of  Meat 

The  most  expensive  item  in  food  is  frequently 
the  meat,  even  when  care  is  taken  in  its  purchase. 

The  following  shows  the  weight  of  the  various  cuts, 
and  the  retail  price  per  pound: 


1.  Porterhouse 

2.  Sirloin 

3.  Round 

4.  Top  Sirloin 

5.  Rib  Roast 


54  Ib.  ©  32^ 
45  "  "  30" 

37K  "  "  28" 
24  "  "  26" 
40  "  "  24" 


330         WALSH'S  BUSINESS  ARITHMETIC 

6.  Rump  21  "  "  24" 

7.  Cross  Rib  12^  "  "  24" 

8.  Flank  4}£  "  "  20" 

9.  Chuck  52^  "  "  20" 

10.  Blade  15  "  "  20" 

11.  Shoulder  12  "  "  19" 

12.  Neck  12  "  "  18" 

13.  Brisket  20  "  "  15" 

14.  Plate  72  "  "  15" 

15.  Navel  48  "  "  15" 

16.  Shin  30  "  "  12 


" 


WRITTEN  EXERCISES 

1.  Find  (a)  the  total  weight  of  the  foregoing  cuts; 
(6)  the  amount  paid;    (c)  the  average  price  a  pound. 
(d)   How  many  pounds  are  sold  above  the  average 
price?     (e)  How  many  below? 

2.  What  is  the  total  amount  obtained  by  the  butcher 
if  he  receives  6  cents  a  pound  for  25  pounds  of  suet, 
3  cents  a  pound  for  25  pounds  of  scraps,  and  %  cent  a 
pound  for  40  pounds  of  bones? 

3.  What   is  the   average   price  a   pound    received 
for   the   entire   carcass,    including   suet,   scraps,    and 
bone? 

4.  What  per  cent  of  the  live  weight  of  1000  pounds 
is  the  weight  of  the  carcass? 

6.  (a)  What  did  the  butcher  pay  for  the  meat  at 
$7.50  per  100  pounds?  (6)  How  much  more  did  he 
receive  for  it? 

6.  How  many  live  cattle  weighing  1000  pounds 
each  will  be  required  to  supply  a  day's  rations  for 


PRODUCTION  AND  CONSUMPTION         331 

6000  men  at  1%  pounds  per  man  if  the  dressed  weight 
of  the  cattle  is  60  %  of  the  live  weight? 

7.  Complete  the  following  table,  which  shows  the 
daily  food  of  528  students  in  a  Government  school, 
at  contract  prices  before  the  war: 


Article 

Total  Food           Oz.  per  pupil 

Price 
per  Ib. 

Total 
Cost 

Bread 

891    Ib. 

5£ 

Beef 

379%  " 

8^ 

Oatmeal 

33     " 

40 

Potatoes 

247%  " 

2jf 

Sugar 

10%  '" 

60 

Sirup 

5%  " 

80 

Corhstarch 

11     " 

So 

Corn  Bread 

i  c)  i      « 

H 

Butter 

16%  " 

30^f 

Flour 

88     " 

4%^ 

Milk 

181%  " 

3£ 

Coffee 

5%  " 

16^ 

Tea 

1/J52  " 

32^ 

Onions 

11        " 

4^ 

Raisins 

11        " 

V 

Tomatoes 

5%  " 

ji 

Total     (a)  (6)  (c) 

8.  Find  (a)  the  total  weight  of  the  daily  rations  for 
528  pupils;  (b)  the  number  of  ounces  to  a  pupil's 
daily  ration;  (c)  the  total  cost  of  528  rations;  (d)  the 
cost  for  each  pupil  each  day. 

ORAL  PROBLEMS 

1.  How  many  cents  a  day  is  the  cost  of  a  wife's 
food  if  it  is  .8  of  the  cost  of  her  husband's  food,  which 
is  30  cents? 


332         WALSH'S  BUSINESS  ARITHMETIC 

2.  How  many  times  the  cost  of  the  father's  food  is 
that  of  the  family  consisting  of  the  parents  and  their 
three  children,  if  the  mother's  food  is  .8  of  that  of  the 
father,  and  the  food  of  the  children  is  .7,  .6,  and  .5, 
respectively,  that  of  the  father? 

3.  Multiply  30  cents  by  3.6. 

4.  When    three   ounces    of   sausage   cake   cost    3% 
cents,  what  was  the  cost  (a)  of  an  ounce?     (b)  Of  a 
pound? 

5.  How  much  starch  is  lost  by  peeling  a  4-ounce 
potato  before  boiling,  if  it   loses  2.7%  when    peeled 
and  .2%  when  boiled  with  skin? 

6.  (a)  When  round  roast  costs  30  cents  a  pound, 
and  4  ounces  are  lost  in  the  bones  and  fat  not  eaten 
what  is  the  cost  an  ounce  of  the  cooked  meat  that 
is  eaten?     (b)  What  per  cent  is  waste? 

7.  If  rib  roast  beef  costs  40   cents   a  pound  un- 
cooked, and  the  waste  is  50%  what  is  the  cost  (a)  of 
a  pound  of  cooked  meat?     (b)  Of  an  ounce? 

8.  How  much  is  saved  on  a  pound  of  cooked  meat 
if  round  roast  costing   30  cents   a  pound   uncooked 
is  used  instead  of  rib  roast? 

9.  To   a   detachment   of   6000   men   the   following 
items  are  issued: 

Tomatoes,  7500  Ib.          Dried  peaches,  48  Ib. 
Onions,  1500  Ib.  Jam,  75  Ib. 

Express  the  weight  of  each  for  a  man  (a)  in  pounds  or 
decimal  of  a  pound,     (b)  In  ounces  or  decimal. 

10.  Give  the  per  cent  of  waste  in  a  pound  of  st<  ak 
that  contains  ten  ounces  of  lean  meat. 


PRODUCTION  AND  CONSUMPTION         333 
RED  CROSS  ARTICLES 

WRITTEN  EXERCISES 

1.  Find  the  value  of  the  materials  used  by  the 
children  of  a  small  school  in  making  the  following 
articles  for  soldiers'  use: 

a  24  pajamas,  each  requiring  6  yards  outing  flannel 

at  12  cents  a  yard; 
7  buttons  at  10  cents  a  dozen; 
1%  yards  of  tape  at  4  cents  per  4-yard  piece. 

The  following  were  used  in  making  all  of  the  pajamas : 
iy2  doz.  spools  of  cotton  at  45  cents  a  dozen; 
50  needles  at  5  cents  a  paper  of  25; 
2000  pins  at  10  cents  a  M; 
5  24  operating  gowns,  each  requiring  5  yards  twilled 

muslin  at  26  cents  a  yard; 
\%  yd.  tape  at  4  cents  a  4-yard  piece. 

The  following  were  used  in  making  all  of  the  gowns : 
1  doz.  spools  of  cotton  at  45  cents  a  dozen; 
50  needles  at  5  cents  a  paper  of  25 ; 
1000  pins  at  10  cents  a  M. 
c  20  bed  shirts,  each  requiring  4%  yards  of  twilled 

muslin  at  26  cents  a  yard; 
1%  yards  of  tape  at  4  cents  a  4-yard  piece. 

The  following  were  used  in  making  all  of  the  shirts: 
10  spools  of  cotton  at  45  cents  a  dozen; 
50  needles  at  5  cents  a  paper  of  25; 
800  pins  at  10  cents  a  M. 

d  120  operating  caps,  each  requiring  %  yard  of  twilled 
muslin  at  26  cents  a  yard. 


334          WALSH'S  BUSINESS  ARITHMETIC 

The  following  were  used  in  making  all  of  the  caps : 
10  spools  of  cotton  at  45  cents  a  dozen; 
50  needles  at  5  cents  a  paper  of  25; 
500  pins  at  10  cents  a  M. 

e  80  operating  helmets,  each  requiring  %  yard  of 
cheese-cloth  at  22  cents  a  yard; 

1  yard  of  tape  at  7  cents  a  4-yard  piece; 
Cotton,  needles,  and  pins  as  in  (d). 

/  80  ice-bag  covers,  each  requiring  %  yard  canton 
flannel  at  20  cents  a  yard; 

2  yards  of  tape  at  4  cents  a  4 -yard  piece; 
Cotton,  needles,  etc.  as  in  (d). 

g  120  comfort  bags,  each  requiring  %  yard  of  cre- 
tonne at  25  cents  a  yard; 
1%  yards  of  tape  at  7  cents  a  4-yard  piece; 
Cotton,  needles,  etc.  as  in  (d). 

2.   Find  the  value  of  the  contents   (a)  of  a  bag, 
(6)  of  120  bags. 

1  spool  of  cotton,  white  $0.05 

1      "      "       "      khaki  .05 

1      "      "  darning  cotton  .05 

1  paper  of  needles  .05 
5  darning  needles  at  5  cents  per  paper  of  25 

1  doz.  white  buttons  .05 

1     "    khaki  .05 

1  thimble  .02 

1  pr.  scissors  .10 

1  cake  of  soap  .05 

1  paper  of  pins  .05 

1  paper  of  safety  pins  .05 


PRODUCTION  AND  CONSUMPTION         335 

1  comb  .15 

1  tooth  brush  .25 

1  small  mirror  .25 

6  handkerchiefs  @  25{£  a  package  of  3 

1  lead  pencil  .02 

1  writing  pad  .10 

24  envelopes  @  3£  a  dozen 

10  postal  cards  @  2^ 

1  collapsible  drinking  cup  .10 

1  pen  knife  .50 

2  pr.  tan  shoe  laces  @  10^ 

3.  How  many  articles  were  made? 

4.  Find  the  total  value  of  the  materials,  and  the 
contents  of  the  bags,  all  of  which  were  contributed 
by  friends  of  the  school. 

THE  MILLINERY  CLASS 

1.  Find  the  cost  of  the  materials  used  in  making 
a  silk-covered  hat  as  follows: 

%  yd.  buckram  at  $3.08  a  roll  of  16  yd. 

3  "    brace  wire  at  12  cents  a  roll  of  30  yd. 
}s    "    crinoline  at  7  cents  a  yd. 

\%    "    satin  at  $1.48  a  yd.  (trimming) 

For  20  hats  there  were  needed : 

4  spools  Kerr's  thread  at  14  cents 
40  milliners'  needles  at  $1.125  a  M. 

2.  Find  the  cost  of  a  straw  hat,  as  follows: 
10    yd.  brace  wire  at  12  cents  a  30-yd.  roll 

%    "  cape  net  at  25  cents 
1%  pc.  straw  braid  at  $1.25 


336          WALSH'S  BUSINESS  ARITHMETIC 

3.   Find  the  cost  of  the  materials  used  in  making 
a  spray  of  three  poppies,  each  flower  requiring: 
%  yd.  ribbon  at  52  cents 
3  centers  at  72  cents  a  gross 
1%  yd.  tie  wire  at  11  cents  a  25-yd.  spool 
1  spray  of  leaves  at  65  cents  a  dozen. 
3  stems  at  36  cents  a  gross  (144) 


ONE  FORM  OF  A  HOUSEHOLD  ACCOUNT 

Mrs.  Goldstone  keeps  her  accounts  in  an  ordinary 
blankbook.  She  gives  a  double  page  to  each  month, 
and  groups  the  monthly  summaries  on  the  thirteenth 
page,  from  which  she  ascertains  the  receipts  and  the 
expenditures  for  the  year. 

The  receipts  are  chiefly  Mr.  Goldstone's  regular 
weekly  salary  of  $25,  which  is  supplemented  by  pay 
for  extra  work,  and  by  interest  on  his  savings. 

Mrs.  Goldstone  makes  her  entries  at  the  close  of 
each  day.  On  June  1,  she  first  writes  37.34,  the 
balance  remaining  at  the  close  of  May  31.  She  then 
enters  her  two  expenditures,  from  the  total  of  which 
she  finds  that  the  balance  then  on  hand  should  be 
35.84.  Finding  that  this  agrees  with  the  cash,  she 
knows  that  she  has  omitted  no  expenditure.  Then 
she  enters  1.50  in  the  "Total"  column,  and  35.84  in 
the  last  one. 

In  making  her  entries  at  the  close  of  June  7,  she 
writes  28.00  in  the  second  column,  as  the  day's  cash 
receipts,  placing  9.38,  the  previous  day's  balance, 
in  the  first  column. 


PRODUCTION  AND  CONSUMPTION        337 

In  the  monthly  "Summary,"  she  inserts  the  total 
of  each  column  except  the  first,  the  third,  and  the 
last.  In  the  first,  she  writes  the  balance  on  hand  at 
the  close  of  May.  In  the  third  she  writes  the  sum  of 
this  balance  and  the  total  receipts  of  the  month.  In 
the  last  column  she  writes  the  difference  between  the 
summary  of  the  third  column  and  that  of  the  next 
column  to  the  last,  which  gives  the  total  expenditures 
of  the  month. 

On  succeeding  pages  is  shown  the  June  page  of  Mrs. 
Goldstone's  account. 

WRITTEN  EXERCISES 

1.  (a)  Find  the  total  of  each   day's  expenditures, 
and  the  balance  at  the  close  of  each  day.     (6)  Find  the 
monthly  summary  of  each  item  of  expenditure,  and 
of  the  total  expenditure,     (c)  Write  the  summary  for 
June;    underneath   it,   write   the   May   summary,   as 
given   below;    on   the  following   lines   insert   the   in- 
crease  or   the   decrease   with   respect   to    each   item. 
(d)  Determine  the  balance  on  hand  at  the  close  of 
April  30,  from  the  data  given  in  the  May  summary. 

2.  Mr.  Goldstone's  income  for  the  year  was  $1440. 
(a)  What  per  cent  of  this  sum  was  spent  during  the  year 
for  rent  at  the  monthly  rate  of  $18?     (6)  What  per 
cent  of  the  June  income  was  spent  for  food  during  that 
month?     (c)  What  per  cent  was  spent  for  food  during 
the  year  if  the  monthly  average  was  $43.20? 

3.  The  cost  of  the  family's  clothing  for  the  year  was 
$352.     What  per  cent  of  Mr.  Goldstone's  income  was 
expended  for  this  purpose? 


338 


WALSH'S  BUSINESS  ARITHMETIC 


JUNE,  1919 


C-21 


On  Hand 

Expenditures 

Day 

Balance 

Receipts 

Total 

Food 

Rent 

Clothing 

Fuel 

Light 

1 

37.34 

2 

35.84 

3.14 

18.— 

3 

.20 

4 

4.30 

5 

6 

.15 

7 

9.38 

28.— 

37.38 

9.80 

8 

9 

2.60 

7.25 

10 

.65 

11 

5.70 

.63 

12 

13 

14 

25.— 

8.74 

15 

1.10 

16 

17 

1.15 

18 

8.— 

19 

20 

21 

29.40 

9.20 

22 

23 

.12 

24 

25 

26 

.27 

27 

28 

25.— 

7.65 

29 

30 

.59 

Summary 

113.10 

150.44 

Last  month 

37.34 

136.10 

48.15 

18.— 

16.30 

2.10 

1.30 

Increase 

Decrease 

PRODUCTION  AND  CONSUMPTION         339 


Balance 

Insur- 
ance 

Ch'rch 

Ice 

Read- 
ing 

Uten- 
sils 

Recre'- 
tion 

Health 

Sun- 
dries 

Bank 

Dues 

Total 

.35 

1.15 

1.50 

35.84 

.35 

.15 

21.64 

14.20 

.20 

.17 

.35 

9.38 

9.80 

27.58 

.40 

2.— 

.35 

.15 

.25 

1.— 

1.63 

.40 

5.— 

.30 

.35 

.15 

$8.40 

40 

.30 

.42 

.35 

.15 

.25 

.24 

5.— 

.10 

.40 

.23 

2.10 

1.50 

.95 

1.01 

3.15 

3.80 

3.10 

— 

15.— 

1.— 

37.34 

340 


WALSH'S  BUSINESS  ARITHMETIC 


THE  HOUSEHOLD  INVENTORY 

The  following  excerpt  is  taken  from  the  Standard 
Fire  Insurance  Policy,  used  in  some  states: 


A  FIRE  SCENE 

If  fire  occur,  the  insured  shall  forthwith 
separate  the  damaged  and  undamaged  personal 
property  .  .  .  make  a  complete  inventory  of 
the  same,  stating  the  quantity  and  the  cost  of  each 
article  and  the  amount  claimed  thereon.  .  .  . 

In  order  to  be  able  to  comply  with  this  requirement 
in  the  event  of  a  fire  in  his  home,  Mr.  Helm  has  listed 
in  a  blankbook  an  inventory  of  the  personal  property 
contained  in  his  residence.  This  book  Mr.  Helm 
keeps  with  his  policy  in  his  office  downtown  in  order 


PRODUCTION  AND  CONSUMPTION 


341 


that  they  escape  destruction  in  a  fire  that  may  destroy 
his  property. 

A  page  is  given  to  each  room  and  one  to  the  reca- 
pitulation. Other  pages  contain  itemized  lists  of  the 
"Books,"  "Pictures,"  "Cut  Glass,"  etc.  A  page  of 
"Pictures,"  for  instance,  would  give  the  title  and 
value  of  each  of  the  eleven  (11)  totaled  in  the  parlor 
page  as  worth  $174,  together  with  the  number  and  the 
value  of  all  of  the  others  in  the  house,  specifying  the 
room  in  which  each  is  hung. 

The  inventory  gives  the  cost  of  each  item  with  the 
date  of  purchase.  From  the  latter  may  be  determined 
the  sum  that  should  be  deducted  for  depreciation. 

The  following  is  a  list  of  articles  contained  in  the 
parlor  when  the  inventory  was  made.  As  articles  are 
added  or  removed,  changes  are  noted. 


PARLOR 

Number 

Article 

Date  of  Purchase 

Cost 

Remarks 

1 

Carpet 

XI-16-1908 

$40.— 

7 

Chairs 

« 

82.— 

1 

Clock 

XII-23-1910 

20.— 

Gift 

4 

Curtains 

X-15-1909 

12.— 

3 

Electric  Fixtures 

XI-16-1908 

25.— 

1 

Jardiniere 

5.— 

Gift 

1 

Lamp 

12.— 

Electric 

1 

Mirror 

25.— 

1 

Music  Cabinet 

15.— 

1 

Piano  and  Cover 

375.— 

1 

Piano  Stool 

5.— 

84 

Piano  Music 

Var 

ous 

37.50 

See  List 

11 

Pictures 

175.— 

«      «< 

1 

Portiere 

IX-15-1911 

10.— 

1 

Rug 

« 

12.— 

4 

Shades 

XI-16-1908 

4.— 

2 

Sofas 

" 

40.— 

1 

Statue 

XII-23-1915 

12.— 

Gift 

2 

Tables 

XI-16-1908 

10.- 

342         WALSH'S  BUSINESS  ARITHMETIC 

WRITTEN  EXERCISES 

1.  Find  the  original  value  of  the  contents  of  the 
parlor. 

2.  The  following  shows  the  last  page.     Include  the 
value  of  the  contents  of  the  parlor,  and  ascertain  the 
original  value  of  all  the  furniture. 

RECAPITULATION 

Halls  $127—  Servants' Room  $48  — 

Parlor  Bath  Room  25  — 

Dining  Room  647.50  Laundry  39.50 

Living  Room  765.—  Attic  168.— 

Kitchen  and  Pantry     129.—  Linen  Closet  94.50 

Bedroom     1  347.50  Chests,  etc.  47.80 

2  263.25  Miscellaneous  123.— 

3  189.50                    Total  $ 

3.  Mr.  Helm  insures  the  foregoing  articles  for  $3000, 
at  the  rate  of  55  cents  a  $100,  for  three  years.     What 
is  the  cost  of  the  insurance? 

4.  In  the  event  of  the  total  destruction  of  all  of  the 
articles  by  fire,  what  sum  should  he  receive  from  the 
insurance    company    if    it    deducts    for    depreciation 
25  %  of  the  original  value  of  the  articles? 


CHAPTER  TWO 


PROBLEMS    OF    THE    PRODUCER 

FARMING  AS  A  BUSINESS 

Everybody,  whatever  his  calling,  is  interested  in 
the  success  of  the  6%  millions  of  farmers,  upon  whom 
devolves  the  part 
of  feeding  and 
clothing,  not 
only  themselves 
and  the  remain- 
ing 70%  of  our 
population,  but 
also  many  mil- 
lions in  other 
parts  of  the 
globe. 

The      world's 
welfare  depends 

upon      a      maxi-  A  FARM  HOUSE 

mum      produc- 
tion,  at   reasonable   cost,  with  prices  that  yield  the 
farmer  interest  on  his   capital   and  a  fair  compensa- 
tion for  his  time,  muscle,  and  brains. 

FARM  ACCOUNTS 

While   the  farmer's   accounts   must   necessarily   be 
few  in  number  and  easily  kept,  they  should  show  him 

343 


344 


WALSH'S  BUSINESS  ARITHMETIC 


the  expense  of  production  and  the  profit  or  the  loss 
made  by  the  sale  of  his  products,  giving  as  much 
detail  as  possible. 


THE  INVENTORY 

Many  farmers  limit  their  accounts  to  the  making 
of  an  annual  inventory,  each  of  which  they  compare 
with  the  preceding  one  to  ascertain  what  may  be  the 
profit  or  loss  for  a  year. 

The  following  are  two  annual  inventories. 

INVENTORY  OF  BURGUNDY  FARM 


Jan.  1,  1919 

Jan.  1,  1920 

T. 

items 

Quantity 

Value 

Quantity 

Value 

Real  Estate 

400  A. 

$38,000.— 

400  A. 

$40,000.— 

Cows,  etc. 

59 

3,750.— 

6 

3,573.— 

Hop 

27 

346.— 

37 

396.— 

Donea 

7 

1,200.— 

9 

1,850.— 

Sheep 

87 

624.— 

100 

875.— 

Hens 

167 

107.— 

132 

83.50 

Machinery,  etc. 

— 

1,500.— 

— 

1.350.— 

Corn 

80  bu. 

120.— 

125  bu. 

187.50 

Oats 

200    " 

180.— 

90    " 

81.— 

Potatoes 

40   " 

36.— 

80   " 

80.— 

Hay 

15    T. 

390.— 

24  T. 

576.— 

Silage 

90     " 

360.— 

HOT. 

440.— 

1-W.I 

IK  " 

45.— 

8KT. 

195.— 

Bills  Receivable 

46.— 

— 

Cash 

670.— 

2,148.— 

Total 

(a) 

(•) 

Less  Mortgage 

8,500.— 

6,500.— 

(6) 

(d) 

Last  year 

(6) 

Increase  for  year 

(•) 

PRODUCTION  AND  CONSUMPTION         345 

WRITTEN  PROBLEMS 

1.  (a)  Find  the  value  of  the  land  and  equipment  on 
Jan.  1,  1919.     (b)  The  net  value  after  the  deduction  of 
the  mortgage,    (c)  The  gross  value  Jan.  1,  1920.    (d) 
The  net  value  at  this  date,      (e)  The  increase  in  a  year. 

2.  Find    the    total    value    of    the    following    items, 
which  have  not  been  included  in  the  farm  equipment: 
Furniture,   $2475;    automobile,   $1800;    2  buggies   at 
$75  each;  harness,  etc.,  $95. 

3.  Find  the  value  of  the  machinery,  as  follows: 


1  thresher  $340  1  manure  spreader 

1  binder  135  1  wheat  drill,  hoe  75 

1  mower,  5-ft.  35  1      "         "  ,  disk  60 

1       "       4-ft.  30  2  harrows,  disk  50 

1  roller  12  2         "      ,  spring  tooth  27 

1  dray  2  2         "      ,  spike  tooth  24 

1  hay  loader  60  2  plows,  2-horse  12 

2  hay  racks  20  2  plows,  3-horse  18 

1  weeder  12  2  double  cultivators  50 

2  wagons,  4-horse  120  2  single  14 
1  wagon,  2-horse  50  4  double  shovel  plows  10 
1  corn  planter,  dbl.  r.  40  1  smoothing  harrow  12 
1       "          "  ,  single  12  1  weeder  12 
1  horse  rake,  side  del.  40  1  horse  rake,  spring  tooth   20 

4.  If  10%  should  be  charged  off  for  a  year's  de- 
preciation,  (a)  what  is  the  value  on  Jan.  1,  1920  of 
machinery  worth  $1500  on  Jan.   1,  1919?     (6)  What 
will  be  its  value  on  Jan.  1,  1921? 

5.  (a)  How  much  is  5  %  of  the  inventory  value  of 
Jan.  1,  1919?     (b)  How  much  does  the  year's  increase 
exceed  this  sum? 


346 


WALSH'S  BUSINESS  ARITHMETIC 


6.  Besides  the  profits  shown  by  the  inventory, 
there  should  be  added  $32.50  a  month  for  the  use 
of  the  house,  $450  for  the  vegetables,  eggs,  etc.,  sup- 
plied by  the  farm,  and  $35  for  wood,  etc.,  used  as 
fuel.  How  much  do  these  items  amount  to  in  a  year? 

RECEIPTS  AND  EXPENDITURES 


The   following   table   gives   Mr. 
and  expenditures  for  five  years: 


Appich's    receipts 


Items 

1st  year 

2dyear 

3d  year 

4th  year 

5th  year 

Receipts 

Cattle 

$2084.30 

$200.— 

$500.10 

$1937.60 

$720.80 

Sheep,  lambs,  wool 

460.— 

590.40 

550.— 

550.— 

750.— 

Wheat 

1230.— 

751.— 

1557.— 

1157.— 

1682.40 

Corn 

969.50 

620.— 

1000.— 

750.— 

906.— 

Oats 

— 

— 

— 

60.— 

75.40 

Hay 

•  — 

709.— 

860.— 

905.— 

980.— 

Live  hogs 

135.60 

309.80 

200.— 

475.— 

756.20 

Poultry  &  dairy  pro- 

ducts 

375.— 

403.— 

462.— 

690.10 

698.40 

Wood 

180.25 

— 







Apples 

506.— 

— 

1427.— 

512.40 

1680.80 

Total  Receipts 

(a) 

(6) 

(<0 

(<*) 

_w__ 

Expenditures 

Labor 

$400.— 

$450.— 

$500.— 

$700.— 

$700.— 

Taxes 

150.— 

138.— 

145.— 

140.— 

168.— 

Farm  Supplies 

300.— 

300.— 

300.— 

200.— 

400.— 

Interest 

360.— 

360.— 

344.— 

260.— 

240.— 

Fertilizer 

135.— 

116.50 

147.86 

185.39 

185.39 

Seed 

550.— 

400.— 

600.— 

750.— 

600.— 

Feed 

212.— 

150.— 

150.— 

197.50 

188.— 

Cattle  (for  Feeding) 

1763.— 

— 

— 

781.24 

— 

Hogs  (for  Feeding) 

36.— 

— 

— 

— 

— 

Extra  Labor 

— 

— 

900.— 

— 

418.— 

Total  Expenditures 

(/) 

(d 

W 

(0 

(;) 

Net  Income 

(*) 

(0 

(m) 

(n) 

(•) 

PRODUCTION  AND  CONSUMPTION         347 


7.  Find  the  receipts  for  each  year,  (a)  to  (e). 

8.  Find  the  expenditures,  (/)  to  (j). 

9.  Find  the  net  income,  (k)  to  (o). 

MILK  PRODUCTION 

The  following  table  shows  the  quantity  of  milk 
yielded  by  a  herd  of  27  cows  on  the  farm  of  Mr.  Pop- 
kins,  who  arranges  to  have  the  winter  production  as 
great  as  possible: 


Month 

Quarts 

Rate 

Receipts 

Month 

Quarts 

Rate 

Receipts 

Sep. 

4,606 

yy 

April 

11,226 

si 

Oct. 

5,708 

3K 

May 

9,342 

3 

Nov. 

5,983 

4 

Jun. 

6,253 

3 

Dec. 

10,510 

4 

Jul. 

4,142 

2/4 

Jan. 

13,008 

4 

Aug. 

4,280 

3 

Feb. 

11,858 

4 

Sold 

1,460 

4 

Mar. 

12,467 

4  - 

Used 

2,190 

slA 

Total 

(a) 

(&) 

10.  Find  (a)  the  number  of  quarts  produced  during 
the  year;  (6)  the  receipts,  including  the  value  of  the 
milk  used  in  the  families  of  the  owner  and  two  hired 
men.  (c)  Find  the  average  value  a  quart,  (d)  Find 
the  total  weight  of  the  milk  at  2Xe  pounds  a  quart. 
(e)  Estimate  the  average  number  of  quarts  a  cow  for 
the  year. 

SIGHT  PROBLEMS 

1.  A  farm  worth  $40,000  is  assessed  for  purposes 
of  taxation  at  $24,000.  (a)  What  per  cent  of  the  actual 
value  is  the  assessed  value?  (b)  The  taxes  for  a  year 
are  $168;  what  is  the  tax  rate  on  each  $1000  of  the 
assessed  value? 


348 


WALSH'S  BUSINESS  ARITHMETIC 


2.   Give  the  value  of  each  of  the  following  a  bushel 
or  a  ton,  from  these  data. 


80  bu.  worth  $120 

200     "          "  180 

40     "  96 

90     "  81 

80     "           "  100 

150     "           "  180 


15  tons  worth  $390 

90       "         "       360 

W     "  45 

24        "         "       576 

110        "         "       440 

VA     "         "        195 


3.   In  a  year  $150  is  expended  for  food  for  a  family 
of  five,  and  the  farm  supplies  food  worth  $450.     (a) 

What  is  the 
total  value  of 
the  food?  (6) 
What  per  cent 
of  the  total  is 
supplied  by  the 
farm? 

4.  The  fuel 
consumed  in  a 
year  is  worth 


A   BARN   AND   SILO 


Of  this  there  is  spent  $25  for  coal.  The  re- 
mainder is  supplied  by  the  farm.  What  per  cent  of 
the  annual  expense  does  the  latter  constitute? 

5.  If  an  apple  tree  occupies  a  space  2  rods  by  2 
rods,  (a)  how  many  square  rods  does  it  occupy?     (b) 
How  many  trees  would  there  be  to  an  acre  (160  square 
rods)?     (c)  To  30  acres? 

6.  Give   the  value   of   2400   bushels   (a)   at   $1   a 
bushel,     (b)  At  %  cents  a  bushel,     (c)  At  97#  cents 
a  bushel. 


PRODUCTION  AND  CONSUMPTION         349 


7.  What  would  be  the  cost  of  5  bushels  of  seed  at 
$5%  a  bushel? 

8.  What  is  the  value  of  40  acres  of  land  at  $120 
an  acre?     If  it  is  assessed  at  60%  of  its  value,  what 
is  the  assessed  value? 

9.  Give  the  interest  for  a  year  on  $400  at  6  %. 

COST  OF  A  CROP 

Some  farmers  desire  to  know  more  about  their 
business  than  is  disclosed  by  a  comparison  of  inven- 
tories, or  even  by  a  statement  of  receipts  and  expen- 
ditures. They  wish  to  ascertain  (a)  the  cost  of 
producing  certain  crops,  and  (6)  the  profit,  if  any, 
of  selling  them  at  market  prices. 

WRITTEN  EXERCISES 

The  following  is  a  memorandum  of  expenditures 
before  the  war  for  labor  in  the  production  of  corn  on 
40  acres: 


! 

Labor 

Cost 

Items 

Dates 

Man 
Hours 

Horse 
Hours 

Man 

Horse 

Total 

Plowing 

Mar.  25-Apr.     2 

80 

320 

(a) 

(b) 

(e) 

Disking 
Harrowing 

Apr.     7-Apr.  29 
"     29-May     4 

90 
25 

360 
50 

(a) 
(a) 

1 

w 

Planting 

"      30-   "        5 

30 

60 

(a) 

(6) 

(c 

Harrowing 

May  10-   "      14 

35 

70 

(a) 

(b) 

(c 

Cultivating 

"      27-   "      30 

60 

120 

(a) 

(b) 

(c 

" 

Jun.     3-Jun.     6 

55 

110 

(a) 

(b) 

(e) 

" 

"      14-   "      18 

50 

100 

(a) 

(b) 

(*) 

« 

"      23-Jul.      5 

60 

120 

(a) 

(b) 

(c) 

Picking  seed 

Sep.    27-Oct.     7 

60 

— 

(a) 

(b) 

Husking 

Nov.    2-Nov.  22 

300 

600 

(a) 

(b) 

(c) 

(d) 

(e) 

(/) 

(9} 

(A) 

350 


WALSH'S  BUSINESS  ARITHMETIC 


1.  Find  the  cost  (a)  of  the  man  labor  on  each  item 
at  20  cents  an  hour;    (b)  of  the  horse   labor  at  12K 
cents  an  hour;    (c)  of  the  total  expense  for  labor  on 
each  item,     (d)  Find  the  total  number  of  man  hours; 
(e)  of  horse  hours.     (/)  Find  the  cost  of  the  man  labor; 
(g)  of  the  horse  labor;    (h)  the  total  labor  cost. 

NOTE:  Find  (/)  by  adding  the  (a)  column.  Check  the  result  by  multi- 
plying 20  cents  by  (d).  Find  (g)  by  adding  the  (6)  column.  Check  the 
result  by  multiplying  12^  cents  by  (e).  Find  (h)  by  adding  the  (c)  column. 
Check  the  result  by  comparing  this  total  with  the  sum  of  (/)  and  (0). 

2.  Find  (a)  the  interest  at  6%  on  the  value  of  the 
land,  40  acres  at  $120  an  acre;   (b)  the  taxes  at  $7  a 
$1000  on  the  assessed  value  of  $2880;    (c)  the  cost  of 
5%  bushels  of  seed  at  $5  a  bushel;    (d)  of  8  tons  of 
fertilizer  at  $16   a  ton;    (e)  the  interest   at  6%  on 
$400,  the  value  of  the  machinery  used. 

3.  Make   out   a   statement   in    the   following   form 
showing  the  receipts,  expenditures,  and  profits  from 
the  foregoing  crop. 

FIELD  B  — 40    ACRES  — CORN 


Sold  2400  bu.  @  97J# 

(a) 

Value  of  Stalks 

29 

u 

Total  Receipts 
Labor  costs 

(c) 

ft) 

Fertilizer 

(d) 

Seed 

(e) 

Interest  on  Land  (Rent) 
Taxes 

1 

Interest  on  Equipment 

(h) 

Other  Expenses 

19 

25 

Total  Expenses 

(0 

Pro 

fit 

0*) 

(b)  Write  the  total  value  of  the  crop.     Insert  at 
(c),    (d),   etc.,   the   several   expenditures   specified   in 


PRODUCTION  AND  CONSUMPTION         351 

previous  examples,  and  the  separate  item,  $19.25. 
At  (i)  write  the  total  expenditures.  At  (j)  write  the 
profit. 

4.  From  the  data  given  in  the  previous  examples, 
find  the  cost  of  production  (a)  an  acre;   (b)  a  bushel. 

5.  Fill  in  the  missing  items  in  the  following  account, 
with  an  acre  of  grapes  during  3  years: 


One  Year 
Cleaning  land 
Plants 
Setting  plants 
Fertilizers 
Cultivating 

Total 
Interest  on  (a) 
for  1  yr.  at  6  % 

Carried  forward 

$25.— 
10.— 
1.— 
12.— 
5.— 

Two  Years 
Forward 
Stakes 
Setting  stakes 
Fertilizers 
Cultivating 

Total 
Interest    on   (d) 
for  1  yr.  at  6  % 

Total 
Deduct  sales  of 
5  2  crates®  $2.50 

Balance  forward 

(c) 
7.50 
3.50 
15.50 
16.— 

Three  Years 
Forward 
Cultivating 
Fertilizers 
New  stakes 
Crates  and  pick- 
ing 

Total 
Interest    on    (i) 
for  1  yr.  at  6  % 

Total 
Deduct  sales  of 
75  crates©  $2.50 

Balance 

(*) 
16.— 
15.50 

2.— 

42.75 

(a) 
(&) 

(4) 

to 

(0 

00 

(c) 

(/) 

(<7) 

(*) 

(1) 

(A) 

(m) 

All  of  the  permanent  laborers  on  Mrs.  Bruen's 
farm  are  men  with  families.  Each  is  supplied  with 
a  house,  an  acre  of  ground  for  a  garden,  a  cow  with 
pasture,  and  firewood. 

SIGHT  PROBLEMS 

1.  Frank  Kerr  receives  $200  a  year  in  cash;  the 
use  of  a  house,  which  he  considers  as  the  equivalent 
of  $10  additional  monthly  wages;  with  land  and  cow, 
from  which  he  derives  products  worth  $70  during  the 
year.  What  is  the  value  of  the  foregoing  for  a  year? 


352          WALSH'S  BUSINESS  ARITHMETIC 

2.  His  wages  are  increased  $25,  the  following 
year,  he  is  given  corn  to  the  value  of  $25,  and  he  sells 
$25  worth  of  vegetables.  What  is  his  income  the 
second  year,  including  the  use  of  the  house  and  the 
value  of  the  other  products  obtained  from  the  land, 
cow,  etc.,  which  this  year  were  worth  $80? 


ONE   AND   ONE-HALF   ACRES   IN  TEN   HOURS 

3.  During  the  next  year  he  receives  an  additional 
$25  in  cash,  and  50  bushels  of  corn  worth  $1  a  bushel. 
What  is  his  income  for  the  third  year,  including  the 
use  of  the  house,  and  $120  as  the  value  of  vegetables, 
milk,  etc.,  sold  and  used? 

4.  During  the  fourth  year  he  receives,  in  addition 
to  other  items  given  in  the  third  year,  30  bushels  of 
wheat  worth  $1.50  a  bushel.     What   is  his  income  for 
the  fourth  year? 


PRODUCTION  AND  CONSUMPTION 


353 


5.  Find  the  cost  of  plowing  an  acre  of  land  when 
one  man  at  $2  a  day,  and  4  horses  at  $1.25  each  a 
day,  plow  (a)  2  acres  in  a  day;    (6)  3  acres. 

6.  If  it  requires  80  hours  of  a  man's  work,  and  320 
hours  of  a  horse's  work  to  plow  40  acres,    (a)   how 
many  horses  are  used  to  the  plow?     At  10  hours  a 


TWENTY   ACRES   IN    SIXTEEN   HOURS 


day,  how  many  days  are  required  (6)  to  plow  40  acres? 
(c)  To  plow  5  acres? 

7.  Assuming  that  a  man  and  a  team  can  do  work 
as  follows,  find  (I)  the  number  of  days  of  labor  re- 
quired to  do  each  of  the  following  for  40  acres;  and 
(II)  the  cost  of  each  at  the  rate  of  $2  a  day  for  a 
man,  and  $2.50  for  a  team: 

a  Plowing,  1%  acres  a  day 
b  Disking,  6%      "      "  " 


354          WALSH'S  BUSINESS  ARITHMETIC 

c  Harrowing,  twice,  10  acres  a  day  each  time 

d  Rolling,  13%  acres  a  day 

e  Seeding,  10 

/  Spreading  manure,  X  acre  a  day 

g  Cultivating  three  times,  673  acres  a  day  each 

time 

h  Harvesting,  6%  acres  a  day 

i  Tying  and  shocking,  no  horses,  3^  acres  per  man 
j  Husking,  %  acre  a  day,  per  man,  no  horses 

8.  (a)  How  many  men  and  teams  would  be  required 
to  do  the  plowing  in  5  days?  (6)  How  many  men 
would  be  required  to  do  the  husking  in  8  days? 

WRITTEN  PROBLEMS 

1.  What  are  the  average  yearly  receipts  of  James 
Reed  for  wages,  when  he  is  paid  during  four  years 
$200,  $275,  $350  and  $385  respectively? 

2.  (a)  Find  his  average  yearly  receipts  from  the  sale 
of  vegetables,  milk,  etc.,  which,  for  the  four  years, 
are  $25,  $45,  $70,  and  $95  respectively. 

3.  Find  his  average  yearly  income. 

4.  His  cash  expenditures  for  food  average  $70  per 
year,  the  remainder  being  supplied  by  the  farm.    Mrs. 
Reed  boards  the  temporary  help,  the  profits  on  which 
supply  the  family  clothing.     How  much  is  left  during 
the  four  years  for  expenses  other  than  rent,  food,  and 
clothing? 

5.  Each  of  Mrs.  Bruen's  permanent  hands  works 
2%  hours  on  Sundays  caring  for  the  stock,  3%  hours  on 
each  of  six  holidays,  5%  hours  on  Saturdays,  and  10 


PRODUCTION  AND  CONSUMPTION  355 

hours  on  the  other  days.     How  many  hours  a  year 
does  each  work? 

6.  In    calculating    the    labor    cost    per    man-hour, 
Mrs.   Bruen  determines  the  annual  expenditures  for 
a  man's  yearly  work  from  the  following  data:    Wages, 
supplies,  etc.,  $385;  6%  on  $50  for  use  of  cow;    6% 
on  $250  for  land  for  vegetables  and  pasture;    6%  on 
$1000,  the  cost  of  the  house,  as  rent;   and  $2  for  insur- 
ance, etc.     Find  (a)  the  labor  cost  of  a  man  a  year. 
(6)  Find  the  cost  per  man-hour  based  on  the  number  of 
hours  of  work  in  example  5. 

7.  Find  the  total  expense  of  a  horse  for  a  year, 
covering  6%  interest  on  $275,  its  cost;   feed,  365  days, 
at  30  cents  a  day;  shoeing,  etc.,  $9. 

8.  (a)  If  the  horse  works   1080  hours   in   a  year, 
what  is  the  expense  an  hour?      (6)  What  is  the  ex- 
pense an  hour  if  the  horse  works  only  1000  hours  a 
year? 

9.  Arthur    Gravely    bought    a    tractor    for    $2080. 
What  is  the  yearly  interest  at  6  %  on  its  cost? 

10.  If  the  life  of  the  tractor  is  6%  years,  what  is 
the  average  yearly  loss  by  depreciation? 

11.  Find  the  total  of  the  yearly  interest,  depreci- 
ation, and  repairs  amounting  to  $75.20. 

12.  The  tractor  is  used  for  104  days  at  an  average 
of  12%  hours  a  day.     How  many  hours  of  work  does 
it  furnish  a  year? 

13.  What  is  the  expense  an  hour  of  work  for  in- 
terest, depreciation,  and  repairs? 


SECTION  V 
FROM  THE  PRODUCER  TO  THE  CONSUMER 

CHAPTER  ONE 

BUYING   AND    SELLING    AGENCIES 
SIGHT  EXERCISES 

1.  From  the  following  data  (a)  give  the  price  paid 
for  a  barrel  of  apples  by  the  consumer: 

Farmer  receives  $2.50  Cartage  to  jobber  .15 

Local  buyer's  profit  .25  Jobber's  profit  .25 

Freight  and  refrigeration  .35  Cartage  to  retailer  .25 

Receiver's  profit  .15  Retailer's  profit  1.10 

(6)  What  per  cent  of  the  price  paid  by  the  consumer 
is  received  by  the  farmer?  (c)  What  is  the  total  of  the 
gross  profits  of  the  four  dealers?  (d)  What  per  cent 
does  each  receive  of  the  price  paid  by  the  consumer? 
(e)  What  per  cent  of  this  price  goes  for  freight  and 
refrigeration?  (/)  What  per  cent  for  the  two  cartage 
items? 

2.  When  a  farmer  receives  $1.10  per  100  pounds  for 
onions  that  cost  the  consumer  $2.50,  what  per  cent  of 
this  selling  price  does  the  farmer  receive? 

3.  A   lot  of   cabbage   is   subject   to   the  following 
charges  from  the  farm  to  the  retailer. 

856 


FROM  PRODUCER  TO  CONSUMER         357 

Farmer  receives         $5  per  ton  Jobber's  profit       $3  per  ton 

Freight  charges         10     "     "  Commission  1    "     " 

Refrigerating  5     ."    "  Cartage  2    "     " 

Barrels  and  handling  2     "     "  Wholesaler's  profit  2    ((     " 

(a)  Give  the  total  of  the  foregoing.  (6)  How  much 
a  ton  does  the  retailer  receive,  at  the  rate  of  3£  a 
pound?  What  per  cent  of  the  cost  to  the  customer 
does  the  farmer  receive? 

COMMISSION 

Compensation  received  by  one  person  for  buying 
or  selling  goods  for  another,  for  collecting  money,  for 
selling  real  estate,  etc.,  is  called  a  commission.  The 
person  doing  this  work  is  called  the  agent;  the  person 
for  whom  it  is  done  is  called  the  principal. 

An  agent  receiving  eggs,  butter,  vegetables,  berries, 
etc.,  to  be  sold  for  the  account  of  a  distant  principal  is 
called  a  commission  merchant.  A  shipment  of  this 
kind  is  called  a  consignment,  the  principal  being  the 
consignor  and  the  agent  the  consignee. 

A  CONSIGNMENT  OF  PRODUCE 

A.  T.  Weekes,  of  Marquette,  Kansas,  ships  to  Sulli- 
van and  Conroy,  commission  merchants,  Kansas 
City,  60  cases  of  eggs  and  150  barrels  of  potatoes,  to 
be  sold  for  his  account. 

The  shipper  (consigner)  delivers  the  goods  at  Mar- 
quette to  the  Missouri  Pacific  R.R.  agent,  from  whom 
he  receives  a  bill  of  lading  (receipt),  which  sets  forth 
that  the  railroad  company  has  received  from  A.  T. 


358 


WALSH'S  BUSINESS  ARITHMETIC 


Weekes  the  above-mentioned  items,  to  be  delivered  to 
Sullivan  and  Conroy  upon  surrender  of  the  bill  of 
lading  and  payment  of  the  amount  due  for  freight. 

The  consignees  (Sullivan  and  Conroy)  present  the 
bill  of  lading,  pay  the  freight  bill,  and  transfer  the 
goods  to  their  store.  When  all  the  articles  are  sold, 
they  send  an  account  of  sales  to  Mr.  Weekes  with  a 
check  for  the  sum  due  him. 

ACCOUNT  OF  SALES 

KANSAS  CITY  Mo.,  Aug.  25,  1919 

SULLIVAN  &  CONROY 

Sold  for  account  of  A.  T.  WEEKES, 

Marquette,  Kansas. 
60  cases  Eggs.     150  bbl.  Potatoes. 


1919 

Aug. 

18 

40  cases  Eggs,  1200  doz.       .32 

(a) 

20 

80  bbl.  Potatoes                  3  .  20 

(b) 

23 

20  cases  Eggs,  600  doz.        .31 

14 

24 

70  bbl.  Potatoes                  3.15 

(d) 

(•) 

Charges 

, 

Aug. 

17 

Freight  and  drayage 

123 

75 

25 

Commission,  4  % 

Cf) 

(*) 

Net  proceeds  by  check  in- 

closed 

(A) 

WRITTEN  EXERCISES 

1.  Copy  and  complete  the  foregoing  account.     Insert 
the  extensions  (a)  to  (c?)  and  the  footing  at  (e).     Find 
(/),  which  is  4%  of  (e).    Insert  at  (g)  the  total  charges. 
Find  (h)  by  deducting  (g)  from  (e). 

2.  Make  out  a  check  on  the  First  National  Bank 
for  the  sum  due  Mr.  Weekes. 


FROM  PRODUCER  TO  CONSUMER         359 

3.  Find  the  weight  (a)  of  a  case  of  30  dozen  eggs 
at  22  ounces  per  dozen  eggs  and  adding  8%  pounds 
for  the  weight  of  the  package.    (6)  Of  the  shipment  of 
30  cases. 

4.  Find  the  weight  of  a  barrel  containing  2%  bushels 
of  potatoes  at  60  pounds  to  the  bushel,  adding  21 
pounds  as  the  weight  of  the  barrel. 

•  5.   How  much  less  than  a  minimum  car  load  of  36,000 
pounds  is  there  in  the  total  shipment? 

6.  (a)  What  is  the  commission  at  2}£%  for 'collect- 
ing a  debt  of  $240.75?     (6)  How  much  does  the  agent 
remit  to  his  principal? 

7.  Find  the  commission  on  the  sale  of  a  house  for 
$9750  at  5%  on  $1000,  2%%  on  $4000,  and  1%  on  the 
remainder. 

8.  How  much  should  a  salesman  sell  in  a  year  to 
yield  him  a  commission  of  $5000  at  3%%  on  his  sales? 

9.  An  agent  bought  for  his  principal  60,000  feet 
of  lumber  at  $42  per  1000  ft.     How  much  did  the 
lumber  cost  the  latter  after  he  had  paid  freight  amount- 
ing to  $275  and  the  agent's  commission  of  2%%? 

10.  A    commission    merchant    received    a    consign- 
ment of  60  crates  of  blackberries.     He  sold  20  crates 
at  $2.40  each,  15  crates  at  $2.60,  and  the  remainder 
at  $2.50.     Find  the  net  proceeds  after  the  deduction 
of  charges  amounting  to  $12.75  and  commission  at  5%. 

THE  LOCAL  BUYER 

The  individual  producer  generally  disposes  of  his 
goods  in  the  neighborhood.  His  surplus  eggs  he 
exchanges  for  groceries  at  the  nearest  store.  His 


360          WALSH'S  BUSINESS  ARITHMETIC 

milk  he  sells  to  the  creamery,  his  grain  to  the  owner 
of  the  elevator  at  the  railroad  station,  his  cotton  to 
the  warehouse  man,  his  cattle  to  a  traveling  buyer, 

etc. 

WRITTEN   EXERCISES 

1.  A  farmer  delivered  12  loads  of  wheat  to  an  ele- 
vator.    The    gross    weights    and    the    tares    were    as 
follows : 

Gross  Tare  Gross  Tare  Gross  Tare 

3150  '  1061  3216  1070  3168  1069 

3210  1062  3420  1072  3056  1073 

3095  1064  3175  1073  3384  1067 

Find  (a)  the  total  gross  weight,  (b)  the  total  tare, 
(c)  the  total  net  weight,  (d)  the  sum  received  for  the 
wheat  at  $2.10  a  bushel  (60  lb.). 

2.  How  much  does  a  planter  receive  for  12  bales  of 
cotton,  weighing,  respectively,  523  lb.,  519  lb.,  532  lb., 
527  lb.,  518  lb.,  516  lb.,  517  lb.,  523  lb.,  518  lb.,  525  lb., 
516  lb.,  525  lb.,  when  the  deduction  for  tare  is  22 
pounds  a  bale,  and  the  rate  is  23%  cents  a  pound? 

3.  A  local  buyer  pays  pickers  of  wild  huckleberries 
12    cents    a   quart   for    picking,  and   he  delivers  the 
berries  to  a  local  shipper  at  an  advance  of  2  cents  a 
quart.    The  latter  supplies  crates  holding  32  quart-cups 
and  consigns  the  berries  to  a  commission  merchant. 
Find  the  shipper's  profit  on  a  crate  when  the  berries 
bring   20   cents    a    quart   less    10%    commission;    50 
cents  is  deducted  for  expressage,  and  30  cents  for  the 
cups  and  the  deterioration  of  the  crate. 

4.  Copy    and    complete    the    following    statement 
rendered  by  the  commission  merchant: 


FROM  PRODUCER  TO  CONSUMER         361 


WILMINGTON,  N.  C.,  Aug.  1,  1919 
E.  K.  WILSON 

Fruit  and  Produce  Commission  Merchants 
Sold  for  account  of  Mr.  F.  T.  O'ROURKE, 
Hamlet,  N.  C. 


12/32  Hbs. 
6/32     "  (soft) 

Express 
Commisson 


.20 
.18 


Check  herewith 


(a) 
(b) 


(d) 


(a) 


NOTE:  (a)  12/32  means  12  crates  of  32  quarts  each,  which  bring  20  cents 
per  quart.  (6)  Six  crates  of  32  quarts  each  bring  18  cents  per  quart,  being 
overripe.  Insert  at  c  the  total  receipts. 

At  (d)  insert  expressage  on  18  crates  at  45  cents  per  crate;  at  (e)  the 
commission  at  10%  on  the  receipts  (c);  at  (/),  the  total  of  (d)  and  (e);  at 
(0)  the  difference  between  (c)  and  (/). 

Observe  the  abbreviations  used  in  expressing  12  crates  of  huckleberries, 
each  containing  32  quarts. 

5.  Find  the  weight  of  a  loaded  crate,  when  the 
crate  weighs  8  pounds,  each  quart-cup  1  ounce,  and 
the  berries  1%  pounds  a  quart. 

SELLING  THROUGH  A  BROKER 

Tormey  and  Ryan  are  local  grain  buyers,  at  Fair- 
view,  near  Marquette,  Kansas. 

Wishing  to  sell  three  car  loads  of  No.  2  wheat  in 
Kansas  City,  they  load  it  on  cars  numbered  18790, 
24360,  and  £9411  of  the  Missouri  Pacific  Railroad, 
consigned  to  their  broker,  George  Smith,  notifying 
the  latter  by  the  following  telegram: 

Have  shipped  1800  bu.    2  wheat,  M.  P.,  18790,  24360, 
29411.     Have  drawn  for  $3000. 

The  last  sentence  notifies  the  broker  that  they  have 
made  a  sight  draft  on  him  for  $3000,  which  he  is  to 


362          WALSH'S  BUSINESS  ARITHMETIC 

pay  to  their  credit  at  a  bank  in  Kansas  City,  and 
receive  the  bill  of  lading. 
The  draft  is  in  this  form: 


$3000  %o  Marquette,  Kan.,  July  30,  1919 

At  sight,  pay  to  the  order  of  Ourselves 
Three  Thousand  00/100—  -Dollars 

value  received,  and  charge  to  account  of 

To  George  Smith      1 

v  r*'±—  ir      I  lormey  &  Ryan 

Kansas  City,  Mo.  J 


They  deposit  this  draft  in  The  Farmers  Bank  of 
Marquette,  for  collection  after  indorsing  it  as  follows: 
Pay  to  the  order  of  The  Farmers  Bank 
for  collection  only. 

Tormey  &  Ryan. 

This  draft  they  attach  to  the  bill  of  lading.  The 
Farmers  Bank  indorses  it  over  to  its  Kansas  City 
correspondent  as  follows : 

Pay  to  the  order  of 

The  First  National  Bank,  Kansas  City,  Mo. 

for  collection  only 

The  Farmers  Bank,  Marquette,  Kansas 
A.  T.  Sullivan,  Cashier. 

sending  it  and  the  attached  bill  of  lading  with 
instructions  to  deliver  the  latter  to  George  Smith 
when  he  "takes  up"  the  draft. 

When  the  draft  with  the  bill  of  lading  reaches  The 
First  National  Bank,  it  immediately  notifies  George 


FROM  PRODUCER  TO  CONSUMER 


363 


Smith.  The  latter  pays  $3000  to  the  bank,  receiving 
the  draft  and  the  bill  of  lading.  The  First  National 
Bank  transmits  the  $3000  less  collection  charges  to 
The  Marquette  Bank,  which  places  the  proceeds  to 
the  credit  of  Tormey  &  Ryan. 

As  soon  as  Mr.  Smith  had  learned  by  telegraph 
of  the  consignment,  he  offered  the  wheat  to  Chas. 
Scott  &  Co.,  who  agreed  to  take  it,  on  arrival,  at  $2.15, 
provided  it  proved,  upon  inspection,  to  be  of  No.  2 
grade. 

When  the  wheat  reached  Kansas  City  on  Aug.  5, 
Chas.  Scott  &  Co.  accepted  it,  giving  a  check  for  its 
value  at  its  arrival  weight  of  107,160  pounds. 

George  Smith  rendered  Tormey  &  Ryan  the  follow- 
ing account  of  sale: 

KANSAS  CITY,  No.,  Aug.  6,  1919 
GEORGE  SMITH 
Grain  Receiver 
Sold  for  account  of 

MESSRS.  TORMEY  &  RYAN 
Marquette,  Kan. 


1919 

Aug. 

5 

107,160  #  Wheat  #2            2.15 
Cars  M.  P.  18790,  24360,  29411 

Charges 
Freight  2^                          36.— 
Interest  4  da.  @  6  %            (6) 
Weighing                                .40 
Inspection                              .  35 
Commission                           (c) 

Net  proceeds  to  your  credit 
Draft 
Balance  due  you 

George  Smith 
perK. 

(a) 

GO 

W 

3000 

(/) 

364          WALSH'S  BUSINESS  ARITHMETIC 

WRITTEN  EXERCISES 

1  .  (a)  How  many  bushels  are  there  in  107,160 
pounds  of  wheat?  (b)  Find  its  value  at  $2.15  a 
bushel. 

2.  George    Smith    charges    a   commission    of    \£    a 
bushel,  also  interest  at  6  %  for  4  days  on  $3000.     What 
is  (a)  his  commission?     (b)  The  interest? 

3.  At   2   cents   a   bushel,  for   freight,  what   is   the 
rate  per  100  pounds? 

4.  Copy    and    complete    the    foregoing    statement, 
from  data  given  above:    Observe  that  (d)  is  the  total 
of  the  charges,  that  (e)  is  (a)  less  (d),  and  that  (/)  is 
(e)  less  $3000. 

5.  Write  George  Smith's  check  on  The  First  Na- 
tional Bank  in  settlement  of  his  account  with  Tormey 
&  Ryan. 

BUYING  THROUGH  A  BROKER 

A  broker  acts  as  purchasing  agent  as  well  as  selling 
agent.  George  Smith  having  received  an  order  from 
Burton  &  Billings,  Milwaukee  millers,  to  buy  6000 
bushels  of  wheat  for  their  account,  made  an  agreement 
with  Robert  Black  for  the  delivery  of  the  wheat  at 
$2.17%,  in  Kansas  City  on  cars  "routed"  for  Mil- 
waukee. 

When  the  cars  were  loaded,  Robert  Black  received 
a  bill  of  lading  consigning  the  shipment  to  Burton 
&  Billings,  Milwaukee.  This  bill  he  attached  to  a 
sight  draft  for  the  cost  of  the  wheat,  which  he  de- 
posited for  collection  in  the  Commercial  National 
Bank. 


FROM  PRODUCER  TO  CONSUMER         365 

George  Smith  notified  his  principals  by  telegraph 
of  the  purchase,  and  mailed  his  bill  of  $60  for  com- 
mission. 

In  this  transaction  the  broker  did  not  handle  the 
money  paid  for  the  wheat.  He  gave  the  millers' 
order  to  Robert  Black,  and  received  his  commission 
from  them.  Mr.  Black  collected  the  value  of  the 
wheat  from  the  consignees  by  means  of  a  draft. 

WRITTEN  EXERCISES 

1.  Find   (a)  the  cost  of  6000  bushels  of  wheat  at 
$2.17%.     (6)  The  freight  at  6  cents  per  100  pounds, 
(c)  The  total  cost  in  Milwaukee  including  freight  and 
commission. 

2.  (a)  Make  out  the  sight  draft  drawn  by  Robert 
Black  on  Burton  &  Billings,     (b)  Write  the  indorse- 
ments transferring  it  to  The  Commercial   Bank   for 
collection,  and  the  latter 's  indorsement,  for  collection, 
to  the  Wisconsin  Trust  Co.,  of  Milwaukee. 

3.  Ryan  &  Co.,  brokers  of  Savannah,  bought  for 
a  Lowell  mill  800  bales  of  cotton  weighing  394,000 
pounds  at  23J^  delivered  to  a  steamer.     Find  the  cost 
of  the  cotton  and  the  commission  of  $5  per  100  bales. 

STORAGE 

Railroad  companies  require  the  removal  of  goods 
from  their  cars  within,  say,  48  hours  after  arrival 
at  terminus.  If  such  merchandise  is  not  intended  for 
immediate  sale,  it  is  stored  in  a  warehouse.  Butter, 
eggs,  poultry,  etc.,  are  bought  by  dealers  at  low  rates 
and  placed  in  cold  storage  until  higher  prices  enable 
the  dealers  to  withdraw  them  for  sale  at  a  profit. 


366          WALSH'S  BUSINESS  ARITHMETIC 

WRITTEN  EXERCISES 

1.  A  dealer  stored  175  cases  of  eggs  for  5  months 
at  the  following  rates : 

For  the  first    25  cases,  20  cents  a  month 
"      "  next   25       "     18     "      " 
"      "  third  25       "     16     "      " 

For  each  additional  25  cases  2  cents  less  a 
month  than  the  rate  for  the  previous  25.  What  was 
the  cost  of  storage? 

2.  Find  the  cost  of  storing  1875  pounds  of  poultry 
for  3  months,  at  %£  a  pound  for  the  first  month  and 
Kj£  a  pound  thereafter. 

3.  (a)  Find  the  cost  of  storing  40,000  bushels  of 
wheat    for    40    days    at  %£    a   bushel    for  receiving, 
weighing,  and  storing  for  10  days;   and  Y$  a  bushel 
for  each  succeeding  5  days.     (6)  Find  the  cost  of  screen- 
ing and  blowing  it  at  %£  a   bushel,  and   delivering 
it  to  an  ocean  vessel  at  %£  a  bushel. 

4.  What  is  the  difference  in  the  expense  of  the  stor- 
age in  the  last  example,  and  the  rate  in  another  ware- 
house of  1^  a  bushel  for  20  days  and  Mo  a  bushel  for 
each  subsequent  day? 


CHAPTER  TWO 

TRANSPORTATION    PROBLEMS 
SIGHT  EXERCISES 

1.  Assuming    1000    pounds,    including    wagon,    as 
the  reasonable  load  for  a  mule  to  draw  for  10  hours  on 
a  level  dirt  road,  (a)  how  many  pounds  can  2  mules 
draw  on  a  wagon  weighing  1000  pounds?     (6)  4  mules, 
on  a  wagon  weighing  1500  pounds?     (c)  6  mules,  on 
a  wagon  weighing  2000  pounds? 

2.  Find  the  rate  per  ton-mile   (1  ton  for  1  mile) 
when  it  costs  $1  to  transport   1   ton  (a)  for  4  miles 
by  horse  and  wagon;     (6)  for   125  miles  by  rail;    (c) 
333K  miles  by  canal;     (d)    1500  miles  on  the  Great 
Lakes. 

3.  A  team  that  can  haul  a  load  of  3000  pounds, 
including  a  1000-pound  wagon,  on  a  level  dirt  road, 
can  haul  5000  pounds  on  the  same  road  after  it  is 
macadamized.     What  part  of  the  expense  of  trans- 
portation is  saved  by  the  improvement  of  the  road, 
assuming  that  the  same  wagon  is  used? 

4.  Find  the  cost   (a)   of  9  pounds  of  oats  at  80 
cents  a  bushel  of   32   pounds,     (b)  Of  12  pounds  of 
oats.      (c)    Of    14   pounds    of  hay  at  $1.25  per  100 
pounds. 

367 


368          WALSH'S  BUSINESS  ARITHMETIC 

6.  Find  the  cost  of  hauling  wheat  when  the  time 
required  to  make  the  round  trip  was  10  hours,  at 
the  cost  of  30  cents  per  man-hour  for  the  driver 
and  6  cents  per  mule-hour  for  each  of  a  pair  of 
mules. 

6.  When  the  load  consisted  of  20  bushels  and  the 
distance  to  the  station  is  10  miles,  give  (a)  the  number 
of  ton -miles;    (b)  the  cost  per  ton-mile;    (c)  the  cost 
per  bushel. 

NOTE:  In  estimating  the  number  of  ton-miles  ignore  the  weight  of  the 
wagon;  also  the  length  of  the  return  trip  with  the  empty  wagon. 

7.  How  many  pounds  does  a  mule  draw  on  rails 
when  his  load  consists  of  3  cars  each  weighing  4000 
pounds  and  con  taming  3000  pounds  of  coal? 

8.  How  many  tons  are  there  in  a  canal  boat  load 
of  8000  bushels  of  wheat? 

9.  How  many  ton-miles  are  represented  by  a  canal 
boat  containing  240  tons  of  freight  and  going  2  miles 
an  hour  for  24  hours?     If  4  mules  are  used,  how  many 
ton-miles  are  obtained  a  mule? 

10.  At  2  miles  an  hour  (a)  how  many  hours  would 
it  require  a  mule-drawn  boat  to  travel  288  miles? 
(b)  How  many  days? 


ANIMAL  TRANSPORTATION 

WRITTEN  EXERCISES 

1.   An  army  mule's  daily  ration  is  9  pounds  of  oats 
and  14  pounds  of  hay.     (a)  Find  the  daily  cost  at  80 


FROM  PRODUCER  TO  CONSUMER         369 

cents  a  bushel  of  32  pounds  for  oats,  and  $1.25 
per  hundred  pounds  for  hay.  (b)  Find  the  cost  for 
365  days,  including  100  pounds  of  straw  monthly  for 
bedding  at  80  cents  per  hundred  pounds. 

2.  Find  the  yearly  cost  of  keeping  a  horse  whose 
daily  ration  is  12  pounds  of  oats  and  14  pounds  of 
hay.     Use  the  foregoing  prices,  and  include  the  cost 
of  bedding  as  above. 

3.  A  planter's  figures  show  that  it  cost  44   cents 
a  day  for  a  mule's  feed  for  210  days,  and  12  cents 
a  day  for  pasture,  etc.,  for  155  days,      (a)  Find  the 
cost   for   the   mule's   keep    a    year   after    adding   $1 
a  month   for    interest,    depreciation,    etc.      (6)  Find 
the    cost  a    mule-hour    when    it    works    2000    hours 
a  year. 

4.  (a)  Find  the  cost  of  transporting  20  bushels  of 
wheat  to  the  railroad  station  when  it  requires  10  hours 
to  make  the  round  trip  at  30  cents  an  hour  for  the 
driver  and  12  cents  an  hour  for  the  team.     (6)  What 
is  the  cost  a  bushel?     (c)  If  the  farm  is  10  miles  from 
the  station,  how  many  ton-miles  are  represented  by  a 
load  of  1200  pounds  hauled  10  miles?     (d)  What  is  the 
cost  per  ton-mile? 

5.  A  mule  travels   3  miles  an  hour  for  8  hours  a 
day,  drawing  3  car  loads  of  coal  from  the  vein  to  the 
shaft  and  returning  with  the  empty  cars.     If  each 
loaded  car  contains   1%  tons  of  coal   (a)   how  many 
ton-miles  are  represented  by  the  loads  drawn  in  4 
hours?      (b)  Give    the    cost    a    ton-mile,   if    the    boy 
driver  receives  $2  a  day  and  the  mule's  work  is  con- 
sidered to  be  worth  70  cents  a  day. 


370          WALSH'S  BUSINESS  ARITHMETIC 

IMPROVED  ROADS 

6.  Mr.   Wilson    hauls   on    an    average    64    tons   a 
year   a   distance  of  5%  miles,     (a)    How  many  ton- 
miles  does  this   represent?      (6)   What  is  his   annual 
saving  in   the  cost  of  hauling,  by  the  reduction  of 
18%   cents    a    ton-mile    by    the    improvement    of  his 
road?     His  share  of  the  cost  of  the  improvement  was 
$375.      (c)   What  per  cent  of  this  amount  is  the  an- 
nual saving? 

7.  The  year  following  the  improvement  of  the  roads 
of  Bagnell  County  100,000  tons  of  freight  were  hauled 
an  average  distance  of  7%  miles  at  a  reduction  of  17% 
cents  a  ton-mile   in  the  cost  of    transportation,     (a) 
What  was  the  saving?     The  improvement  of  the  120 
miles  of  roads  cost  $1750  a  mile.     The  value  of  the 
property  in  the  county  was  $18,000,000.     (6)  What  per 
cent  of  the  value  of  the  property  did  the  improvement 
cost?     (c)  What  was  Mr.  Bradford's  share  of  the  cost, 
if  his  farm  of   160  acres  was  valued  at  $112.50  an 
acre? 

8.  (a)  How  many  square  yards   are   there  in   the 
surface  of   a   road  a  mile  (1760  yards)  long  and  15 
feet  wide?     (b)   If  a  ton  of  broken  stone  will  cover  3% 
square  yards  to  the  proper  depth,  how  many  tons 
will  be  required  for  a  mile  of  road? 


RAILROAD  TRANSPORTATION 

The  freight  rates  between  Missoula  and  Portland, 
Oregon,  are  as  follows: 


FROM  PRODUCER  TO  CONSUMER         371 

1st  class  $1.60  a  100  Ib.  Furniture,  Dry  Goods,  etc. 

2d    .  "  1.36  "  "     "  Hardware,  Copper,  etc. 

3d       "  1.12  "  "     "  Paint,  Plow  Points,  etc. 

4th     "  .96  "  "     "  Canned  Vegetables,  etc. 

5th     "  .80  "  "     "  Wrapping  Paper,  etc. 


There  are  four  other  classes,  A,  B,  C,  and  D,  the 
rates  being  64^,  48^,  40^,  and  32  j£,  respectively. 

9.   Find  the  cost  a  ton-mile  at  each  of  the  fore- 
going rates  from  Missoula  to  Portland,  634  miles.    * 

10.  Find   the   freight   from   Missoula   to   Portland, 
for  an  automobile  weighing  2750  pounds,  when  the  rate 
is  double  the  1st  class  one. 

11.  The  freight  rates  from  Denver  to  Salt  Lake 
City,  745.5  miles,  are  as  follows  a  100  pounds: 

1st  class,  $1.54;  2d  class,  $1.31;  3d  class,  $1.15; 
4th  class,  $  .96;  5th  class,  $  .79%.  Find  the  rate  a 
ton-mile  for  each  class. 

12.  The  rate  on  fruit  for  less  than  car  loads  (L.C.L.) 
is  $1.54  a  100  pounds;  for  car-load  lots  (C.L.),  it  is  $1 
a  100  pounds.     What  per  cent  of  the  former  rate  is 
the  latter? 

13.  How  much  will  a  shipper  of  18,690  pounds  of 
fruit  (and  packages)  save  by  paying  $1  a  100  pounds 
for  a  car  load  of  24,000  pounds,  instead  of  the  L.C.L. 
rate  of  $1.54  a  100  pounds  on  the  actual  weight  of  the 
shipment? 

COMMODITY  RATES 

In  addition  to  the  100-lb.  rate  for  ordinary  freight, 
there  is  frequently  a  "commodity  "  rate  for  such  articles 


372          WALSH'S  BUSINESS  ARITHMETIC 

as  grain,   which  pays  by  the  bushel;    coal,   by  the 
ton;   milk,  by  the  40-quart  can,  etc. 

WATER  TRANSPORTATION 

1.  (a)  How  many  tons  are  there  in  a  Lake  steamer 
load  of  400,000  bushels  of  wheat?      (6)  How  many 
freight  cars  containing  36,000  pounds  each  are  needed 
to  transport  this  quantity  of  wheat?     (c)  How  many 
such  steamer  loads  will  be  required  to  fill  a  tow  of  48 
barges,  each  having  a  capacity  of  1000  short  tons? 

2.  Find  the  cost  of  transferring  400,000  bushels  of 
wheat  from  canal  boats  to  an  ocean  steamer  as  fol- 
lows: 

Harbor  towing,  $4  a  boat  of  8,000  bushels 
Transportation  of  floating  elevator,  }$  a  bushel 
Weighing  and  transferring,  %£  a  bushel 
Trimming  on  canal  boat,  $1.50  a  1000  bushels 
Trimming  on  steamer,  $2. —  a  1000  bushels 

3.  (a)  When  the  rail  freight  rate  was  16  cents  a 
100  pounds  from  Chicago  to  New  York,  what  was  the 
rate  a  bushel?     (b)  How  much  less  a  bushel  would  it 
cost  at  1.2^  a  bushel  by  lake  from  Chicago  to  Buffalo, 
Kj£  a  bushel  for  transferring  from  steamer  to  canal 
boat;   and  5^  a  bushel  by  canal  boat  from  Buffalo  to 
New  York? 

4.  At  9.6  cents  for  the  freight  on  a  bushel  of  wheat 
for  960  miles,  what  is  the  rate  a  ton-mile? 

5.  Find  (a)  the  canal  (and  river)  rate  a  ton-mile 
when  the  cost  for  transporting  a  bushel  of  wheat  was 
.44^  for  440  miles,     (b)  The  ocean  rate  a  ton-mile 
when  the  cost  was  6    for  a  bushel  1800  miles. 


FROM  PRODUCER  TO  CONSUMER         373 

6.  When  the  steamboat  rate  on  eggs  is  47^   a  100 
pounds   between   Cincinnati  and  Memphis,  find   the 
ton-mile  cost,  taking  (a)  the  distance  by  water,  750 
miles;     (b)   the  land  distance  of  500  miles  by  road. 
(c)  Find  the  ton-mile  rate  by  rail  at  60  cents  a  100 
pounds  for  494  miles. 

7.  How   much   more   would   it   cost   to   ship   5400 
dozen  eggs  in  cases  containing  30  dozen  each  than  in 
cases  containing  36  dozen  each,  when  the  freight  is 
23  cents  a  case  regardless  of  its  weight? 

SHIPMENTS  BY  EXPRESS 

The  minimum  freight  on  a  package  is  the  rate  per 
100  pounds,  while  express  rates  cover  all  weights  from 
a  pound  up. 

The  Union  Express  Company,  which  covers  nearly 
every  section  of  the  United  States,  has  nearly  300 
"scales."  The  "scale"  for  any  office  gives  the  rate 
to  every  other  office  in  the  country. 

Express  packages  are  divided  into  three  classes, 
according  to  their  bulk,  value,  etc.  Most  of  the  pack- 
ages are  of  the  first  class. 

They  are  carried  on  a  car  forming  part  of  a  passenger 
train,  which  insures  rapid  transit.  They  are  delivered 
to  the  stores  or  residences  of  city  consignees. 

SPECIMEN  RATE  SCALES 

The  cost  of  the  expressage  on  a  first-class  package 
to  New  York  from  certain  specified  cities  is  as  follows 
for  certain  weights  up  to  100  pounds. 


374          WALSH'S  BUSINESS  ARITHMETIC 

RATES  TO  NEW  YORK  FROM 


Weights 

Chicago 

St.  Louis 

Dallas 

Denver 

Butte 

San 
Francisco 

lib. 

$0.30 

$.30 

$.33 

$.33 

$.36 

$.38 

2 

.32 

.33 

.38 

.40 

.44 

.49 

3 

.34 

.35 

.44 

.45 

.53 

.60 

4 

.37 

.37 

.49 

.52 

.60 

.73 

5 

.40 

.41 

.55 

.57 

.69    ' 

.84 

6 

.42 

.43 

.60 

.64 

.77 

.95 

7 

.44 

.45 

.65 

.69 

.86 

1.06 

8 

.47 

.48 

.71 

.76 

.93 

1.17 

9 

.49 

.51 

.77 

.81 

1.02 

1.28 

10 

.51 

.53 

.81 

.87 

1.10 

1.39 

20  Ib. 

.75 

.79 

1.36 

1.47 

1.94 

2.51 

30  Ib. 

.98 

1.04 

1.90 

2.07 

2.76 

3.62 

50  Ib. 

1.45 

1.56 

2.99 

3.27 

4.42 

5.85 

100  Ib. 

2.64 

2.86 

5.72 

6.27 

8.58 

11.44 

A  fraction  of  a  pound  is  taken  as  abound. 

WRITTEN  EXERCISES 

1.  Find  the  expressage  to  New  York  on  packages 
from  Chicago  as  follows: 

a  24  weighing  4%  pounds  each. 
b  47  weighing  6)4  pounds  each. 
c  36  weighing  8%  pounds  each. 

2.  Find  the  expressage  to  New  York  on  packages 
from  St.  Louis  as  follows: 

a  137  weighing  3  Ib.  5  oz.  each. 
b  294  weighing  19  Ib.  7  oz.  each. 
c  178  weighing  7  Ib.  5  oz.  each. 

3.  Find  the  expressage  to  New  York  on  the  follow- 
ing packages: 


FROM  PRODUCER  TO  CONSUMER         375 

a  168  from  Dallas,  each  weighing  3^  pounds. 
b  209  from  Denver,  each  weighing  9  Ib.  14  oz. 
c  329  from  Butte,  each  weighing  29%  pounds. 
d  415  from  San  Francisco,  each  weighing  49  Ib.  9  oz. 

4.  A  merchant  shipped  from  New  York  packages 
as  follows,  each  weighing  99  Ib.  1  oz.:  153  to  Chicago, 
217  to  St.  Louis,  98  to  Dallas,  369  to  Denver,  54  to 
Butte,  and  147  to  San  Francisco.  Find  the  total 
charge  for  expressage. 

MAIL  MATTER 

Domestic 

United  States  and  Possessions 

Domestic  mail  matter  is  divided  into  four  classes: 
First  —  Letters,  postal  cards,  sealed  packages. 
Second  —  Periodical  publications. 
Third  —  Miscellaneous    printed    matter    weighing 

four  pounds  or  less 

Fourth  (Parcel  Post)  —  All  mailable  matter  not 
included  in  previous  classes. 

RATES  OF  POSTAGE 
First-class  Matter 

Postal  cards,  1  cent  each.     Letters  and  sealed  pack- 
ages 2  cents  an  ounce  or  fraction  thereof.     Mail  carried 
by  aeroplane,  6  cents  for  the  first  ounce  or  fraction 
thereof,  and  6  cents  for  each  additional  ounce. 
SIGHT  EXERCISES 

1.  Give  the  cost  of  postage  (a)  on  246  letters  each 
weighing  less  than  1  ounce,  (b)  On  122  similar  letters 
weighing  over  1  ounce,  but  less  than  2  ounces. 


376          WALSH'S  BUSINESS  ARITHMETIC 

2.  What  postage  should  you  pay  on  a  sealed  package 
weighing  10  ounces? 

3.  Give  the  cost  of  mailing  25  letters  by  aeroplane 
post,  each  weighing  three  quarters  of  an  ounce. 

Second-class  Matter 

The  rate  of  postage  on  newspapers  and  periodicals 
bearing  notice  of  entry  as .  second-class  matter  and 
sent  unsealed  by  the  public,  is  1  cent  for  each  4  ounces 
or  fraction  thereof. 

4.  Give  the  postage  on  a  newspaper  weighing 
a  1  oz.     b  2%  oz.     c  3%  oz.     d  8%  oz.     e  11  oz. 

5.  Give   the  postage   on   a  package   of  magazines 
weighing 

a  18  oz.     b  %  Ib.  3  oz.     c  3  Ib.  1  oz.     d  5  Ib.  10  oz. 

Third-class  Matter 

The  rate  of  postage  on  circulars,  newspapers,  and 
periodicals  not  entered  as  second-class,  and  other 
printed  matter  (not  books),  is  1  cent  for  2  ounces  or 
fraction  thereof.  Limit  of  weight  is  4  pounds. 

6.  Give  the  postage  on  a  map  weighing 

a  5  oz.     b  3  oz.     c  7  oz.  d    4%  oz.     e  6%  oz.    /  8  oz. 

7.  Give  the  postage  on  a  package  of  pictures  weigh- 
ing 

a  12  oz.     b  1  Ib.  10  oz.     c  3  Ib.  4  oz.     d  2  Ib.  9  oz.     e  21  oz. 

Fourth-class  Matter 

Parcels  weighing  4  ounces  or  less,  except  books, 
seeds,  plants,  etc.,  pay  1  cent  for  each  ounce  or  fraction 
thereof.  Parcels  weighing  8  ounces  or  less,  con- 


FROM  PRODUCER  TO  CONSUMER 


377 


taining   books,  catalogues,  seeds,  plants,  etc.,  pay   1 
cent  for  each  2  ounces  or  fraction  thereof. 

Larger  parcels  of  books,  seeds,  plants,  and  other 
mailable  articles  pay  the  parcel  post  rates  given  on 
another  page.     These  are  based  on  the  weight  of  a 
parcel  and  the  distance  to  which  it  is  to  be  carried. 
8.   Give  the  postage  on  a  package  of  seeds  weighing 
a  1  oz.     b  7  oz.     c  3  oz.     d  8  oz.     e  5  oz.    /  4  oz. 
PARCEL  POST  RATES 


Weight 

Local 
Rates 

1st  and 
2nd  zones 
50  to  150 
mi. 

3d  zone 
150  to 
300  mi. 

4th  zone 
300  to 
600  mi. 

5th  zone 
600  to 
1000  mi. 

6th  zone 
1000  to 
1400  mi. 

7th  zone 
1400  to 
1800  mi. 

8th  zone 
over 
1800  mi. 

lib. 

$0.05 

$0.05 

$0.06 

$0.07 

$0.08 

$0.09 

$0.11 

$0.12 

2 

.06 

.06 

.08 

.11 

.14 

.17 

.21 

.24 

3 

.06 

.07 

.10 

.15 

.20 

.25 

.31 

.36 

4 

.07 

.08 

.12 

.19 

.26 

.33 

.41 

.48 

5 

.07 

.09 

.14 

.23 

.32 

.41 

.51 

.60 

6 

.08 

.10 

.16 

.27 

.38 

.49 

.61 

.72 

7 

.08 

.11 

.18 

.31 

.44 

.57 

.71 

.84 

8 

.09 

.12 

.20 

.35 

.50 

.65 

.81 

.96 

9 

.09 

.13 

.22 

.39 

.56 

.73 

.91 

1.08 

10 

.10 

.14 

.24 

.43 

.62 

.81 

1.01 

1.20 

etc. 

etc. 

etc. 

etc. 

etc. 

etc. 

etc. 

etc. 

etc. 

20  Ib. 

.15 

.24 

.44 

.83 

1.22 

1.61 

etc. 

etc. 

etc. 

etc. 

etc. 

etc. 

etc. 

50  Ib. 

„*.  _ 

.30 

—  JL_ 

.54 

1.04 

2.03 

3.02 

4.01 

etc. 
70  Ib. 

etc. 
.40 

etc. 

.74 

Maximum  weight  50  Ib. 

Maximum  weight  70  Ib. 

9.    Give    the    postage    on    each 
packages  mailed  in  Kansas  City: 


of    the    following 


Place 

Zone 

Weight 

Any  P.  0. 

Zone 

Weiqht 

a 

Pierre,  S.  D. 

4 

9 

Ib. 

13  oz. 

b  In  Alaska 

8 

22 

Ib. 

3  oz. 

c 

Topeka,  Kans. 

1 

69 

Ib. 

d 

Nevada 

6 

9 

oz. 

e 

Peoria,  111. 

3 

17 

Ib. 

4oz. 

f 

S.  C. 

5 

16 

11). 

7  oz. 

<J 

San  Francisco 

7 

33 

Ib. 

8  oz. 

h 

Conn. 

6 

9 

Ib. 

7  oz 

i 

Lincoln,  Neb. 

2 

48 

Ib. 

i 

Hawaii 

8 

14 

oz. 

k 

Kansas  City 

Local 

64 

Ib. 

I 

D.  C. 

5 

27 

Ib. 

CHAPTER  THREE 
PROBLEMS    OF    THE    MANUFACTURER 

MAKING  AND  SELLING  BREAD 

PREPARATORY    EXERCISES 

1.  Mr.    Taylor   purchased   an    established   bakery, 
the  books  of  which  showed  the  following  expenditures 
for  the  preceding  year:  materials,  $4500;  help,  $2920; 
sundry  expenses,  $820.     Give  the  total  expenditures. 

2.  What  was  the  profit  for  the  year  if  the  sales 
amounted  to  $9000? 

3.  Find  the  cost  (a)  of  300  barrels  of  flour  at  $11 
a  bbl.;    (6)   of  60  barrels;    (c)  of  5   barrels;    (d)  of 
365  barrels. 

4.  If  the  total  cost  of  materials  was  $4500,  find  the 
amount  spent  for   the  other   articles:    sugar,   yeast, 
salt,  butter,  eggs,  etc. 

5.  If  16  tons  of  coal  were  used  in  300  working  days, 
how  many  working  days  would  a  ton  last? 

6.  The  rent  of  the  building  is  $40  a  month,  %  of 
which  should  be  charged  to  the  bakeshop   and  %  to 
the  store,     (a)  What  fraction  of  the  rent  remains  to  be 
charged  to  the  living  expenses  of  the  family?     (6)  How 
many  dollars  a  year? 

7.  The  expense  for  help  included  a  baker's  wages 
at  $1200,  the  proprietor's  services  at  $1200,  and  the 
pay  of  a  girl  in  the  store.     How  much  did  she  receive 
(a)  a  year?     (6)  A  week? 

378 


FROM  PRODUCER  TO  CONSUMER 


379 


8.  A  barrel  of  flour  makes  315  pounds  of  dough. 
If  %  of  this  is  lost  in  the  process  of  baking,  (a)  how  many 
pound-loaves  of  bread  does  a  barrel  of   flour  make? 
(b)  How  many  loaves  weighing  14  ounces  each? 

9.  If  $4000  was  received  from  the  yearly  sales  of 
bread  and  rolls,  how  much  was  realized  from  the  sales 
of  pies  and  cakes? 

10.  If  %  of  the  baker's  time  was  spent  in  making 
pies  and  cakes,  how  much  of  his  yearly  pay  should 
be  charged  to  the  labor  on  these? 


MR.  TAYLOR'S  MEMORANDA 
From    the    accounts    of    the    preceding    year, 
Taylor  made  the  following  memorandum  of 

MANUFACTURING  COSTS 


Mr. 


Materials 
Direct  labor 

$4500 
1200 

Flour,  Yeast,  Salt,  Sugar,  Fruit,  etc. 
Wages  of  the  baker 

Prime  cost 
Indirect  labor 
Rent 
Fuel,  light,  etc. 
Depreciation,  etc. 

? 
600 
80 
210 
110 

Sum  of  the  foregoing 
One-half  of  the  proprietor's  services 
One-sixth  of  rent  of  building 
Coal,  gas  bills,  etc. 
Repairs,  insurance,  etc. 

Manufacturing  costs 

? 

Total  of  the  preceding  five  items. 

11.  What  was  the  prime  cost,  which  is   the   total 
spent  for  materials  and  the  pay  of  the  baker? 

12.  What  were  the  overhead  factory   expenses,   the 
sum  of  all  other  items  of  expenditures  incurred  in  pre- 
paring the  articles  for  sale? 

13.  What  fraction  of  the  prime  cost  was  the  over- 
head factory  expense? 

This  fraction  is  called  the  factory  rate  of  burden. 

One-half  of  the  proprietor's  allowance  is  charged  to  the  bakeshop. 


380          WALSH'S  BUSINESS  ARITHMETIC 

Mr.  Taylor  made  another  memorandum  showing 

SELLING  COSTS 


Proprietor's  pay 
Salesgirl's  pay 
Rent 
Heat,  Light,  etc. 
Depreciation,  etc. 

$600 
520 
240 
90 
90 

One-half  of  allowance 
$10  per  week 
One-half  of  $480 
Coal  used  to  heat  store,  gas  bill 
Repairs,  insurance,  etc. 

3,  etc. 

Selling  costs 

? 

Total  of  the  foregoing 

Mr.    Taylor    combined    the    foregoing    memoranda 
into  the  following: 

Statement 

Labor  and  Materials  $5700 

Factory  Expenses  1000 

Selling  Expenses  1540 

Profit  ? 
Received  from  sales 


14.  What  was  the  profit  for  the  year? 

15.  Give  the  rate  per  cent  of  the  profit  on  the  gross 
receipts  from  sales. 

Mr.  Taylor  made  a  detailed  examination  of  the 
manufacturing  and  the  selling  costs  to  determine  the 
percentage  of  profit  on  each  of  the  separate  items  of 
(a)  bread,  (6)  cakes,  and  (c)  pies. 

Two  barrels  of  flour  were  used  on  each  Saturday, 
and  on  the  eve  of  a  holiday,  and  one  on  each  other 
working  day. 

One-half  of  each  barrel  was  used  for  bread,  one- 
third  for  cakes,  and  one-sixth  for  pies,  and  the  cost  of 
the  flour  for  each  was  apportioned  on  this  basis. 
The  cost  of  the  other  materials,  as  shown  by  the  books, 


FROM  PRODUCER  TO  CONSUMER         381 


determined  the  rates  as  given  for  the  cost  of  materials 
in  the  next  table.  The  extra  work  required  in  pre- 
paring cake  and  pie  for  the  oven,  made  one-third  of  the 
baker's  pay  the  proper  charge  for  each,  notwithstand- 
ing the  difference  in  the  respective  quantities  made  of 
the  three  varieties. 

The  extra  space  required  in  preparing  several  kinds 
of  cakes  and  of  pies  over  that  needed  in  mixing  dough, 
called  for  the  given  apportionment  of  rent.  The 
apportionment  for  depreciation  was  made  on  the 
same  basis. 

WRITTEN    EXERCISES 

1.  Complete  the  following  table  of  Mr.  Taylor's 
analysis  of  manufacturing  costs: 

ANALYSIS  OF  MANUFACTURING  COSTS 


Total 

Bread 

Cake 

Pie 

Materials 
Direct  labor 

$4500 
1200 

#5 

K 

% 

H 

K 

K 

Prime  cost 
Indirect  labor 
Rent 
Fuel,  etc. 
Depreciation 

? 
600 
80 
210 
110 

? 
K 
% 
K 
% 

? 
% 

% 
% 
% 

? 
% 

% 
% 
% 

Manufacturing  costs 

? 

? 

? 

? 

The  fractions  indicate  each  item's  part  of  the  total 
in  the  same  line.  Change  these  fractions  to  dollars. 
Give  totals  in  dollars  in  the  spaces  indicated  by  a  ques- 
tion mark  (?) 

2.  Complete  the  following  table  of  Mr.  Taylor's 
statement  of  selling  costs: 


382          WALSH'S  BUSINESS  ARITHMETIC 

ANALYSIS  OF  SELLING  COSTS 


Total 

Bread 

Cake 

Pie 

Proprietor's  allowance 
Salesgirl's  pay 
Rent 
Fuel,  light,  etc. 
Depreciation 

$600 
520 
240 
90 
90 

K 

% 
% 
% 
% 

Ko 
Ko 
X 
X 
X 

X 
X 
X 
X 
X 

Selling  costs 
Manufacturing  costs 

? 
Insert 

? 

'rom  prec 

? 

eding  exam 

? 
pie 

Total  costs 
Receipts  from  sales 

? 
? 

? 
4000 

? 
3000 

? 
2000 

Profit 

? 

? 

? 

? 

3.  (a)  Find  the  cost  of  365  barrels  of  flour  at  the 
average  rate  of  $10.50  a  barrel.     (6)  Find  the  cost  of 
the  other  bread  materials  if  the  total  cost  was  $2100 
including  the  cost  of  one-half  of  the  flour. 

4.  One-third  of  the  flour  was  used  for  cake.     Find 
the  cost  of  the  sugar,  shortening,  eggs,  currants,  etc., 
if  the  total  cost  of  the  cake  ingredients  amounted  to 
$1600. 

6.  The  total  cost  of  the  pie  ingredients  was  $800, 
including  that  of  one-sixth  of  the  flour.  How  much 
was  paid  for  the  remaining  materials? 

6.  From  a  barrel  of  flour  dough  was  made  weighing 
315  pounds,  which  lost  %  of  its  weight  in  baking.    Find 
the  number  of  one-pound  loaves  made  during  the  year. 

7.  Of  the  foregoing,  220  stale  loaves  were  sold  at 
half  price,  and  the  others  at  8  cents  each.     How  much 
was  received  for  the  bread? 

8.  (a)  What  per  cent  of  the  sum  received  from  the 
sales  of  bread  was  the  profit?     (6)  Of  the  sum  received 


FROM  PRODUCER  TO  CONSUMER         383 

from  the  sales  of  cake?   (c)  Of  the  sum  received  from 
the  sales  of  pie? 

9.  (a)  In  order  to  have  made  a  profit  of  12^%  on 
his  cake  sales  of  $3000,  how  much  less  should  have 
been  spent  for  the  materials,  the  other  expenses  re- 
maining the  same?     (6)  What  per  cent  of  the  materials 
used  could  be  obtained  for  this  sum? 

10.  Mr.  Taylor's  predecessor  sold  his  pies  for  £0  cents 
each,     (a)   How  many  pies  did  he  make?     (6)   Find 
the  average  cost  of  a  pie.     (c)  If  he  had  charged  y, 
more  than  this  cost,  what  would  have  been  the  selling 
price  of  a  pie?      (d)  What  per  cent   of   this   selling 
price  would  the  profit  have  been? 

11.  The  following  is  the  cost  sheet  of  a  shirt  factory 
for  a  year: 

FACTORY  COSTS 


Raw  materials 
Direct  labor 

$250,000 
150,000 

(a) 

Prime  cost 

Salaries  of  factory  officials 
Wages 

3,500 
19,500 

(b) 

Total  indirect  labor 

Rent  of  factory 
Power,  light,  heat 
Repairs  to  equipment 
Fire  insurance 
Other  insurance 
Employer's  liability,  etc. 
Welfare  work 
Taxes,  state  and  local 
Other  factory  expense 

8,000 
3,000 
2,000 
1,500 
500 
500 
1,500 
500 
6,000 

Total  factory  expense 

Total  factory  overhead                                                       (d) 

Find   (a),   (6),  and   (c).     Find   (d)  the  total  factory 
overhead  which  is  the  sum  of  the  cost  of  indirect  labor 


384 


WALSH'S  BUSINESS  ARITHMETIC 


(b)  and  of  factory  expense  (c).  Find  (e)  the  rate  of 
burden;  viz.,  the  percentage  the  total  factory  over- 
head (d)  is  of  the  prime  cost  (a). 

Find  (/)  the  administrative  expense  and  (g)  the  sell- 
ing expense  from  the  next  two  tables. 

The  following  sheet  shows  the  expense  of  adminis- 
tration for  a  year. 

ADMINISTRATIVE  EXPENSE 


Salaries  of  officials 
Salaries  of  office  force 
Rent  of  general  office 
Office  expense 
Collecting  expense 
Bad  debts 
Corporation  tax 
Other  administrative  expense 

$6,500 
5,500 
1,500 
500 
2,000 
2,500 
250 
2,250 

Total  administrative  expense 

(/) 

The  following  sheet  shows  for  a  year  the  cost  of 
selling  articles  made  in  the  factory. 


SELLING  EXPENSE 


Salaries  of  officials 
Salaries,  commissions,  etc.,  of  salesman 
Wages 
Rent  of  show  and  shipping  rooms 
Packing  materials 
Cartage  and  freight  outward 
Advertising 
Other  selling  expense 

$6,000 
28,000 
1,500 
2,500 
2,250 
3,250 
5,500 
10,500 

Total  selling  expense 

(f) 

Find  (h)  the  total  cost  of.  manufacturing,  administer- 
ing, and  selling,  including  payments  of  $4500  inter- 
est on  loans  and  $3500  deterioration  on  equipment. 


FROM  PRODUCER  TO  CONSUMER 


385 


(?)    The  net  profit  for   the  year  on  the  sales,  which 
amounted  to  $660,00a.     (j)  The  per  cent  of  $660,000. 
Make  out  a  sheet  in  the  following  form,  taking  the 
amounts  from  (k)  to  (t)  from  the  foregoing  tables: 

STATEMENT  FOR  1920 


Gross  receipts  from  sales 
Raw  materials 
Direct  labor 

0 

(») 

w 

(*) 

Prime  cost 

Indirect  labor 
Factory  expense 

Co) 

Factory  overhead 

Total  manufacturing  expense 

Administrative  expense 
Selling  expense 
Interest  and  deterioration 

w 

Total  expense  of  administration,  selling,  etc. 

Total  gross  cost  of  goods 

w 

Net  profit  for  the  year 

w 

12.   From  the  last  statement  find  the  per  cent  (two 
decimal  places) . 

a  The  cost  of  raw  materials  is  of  the  prime  cost. 
b  The  cost  of  direct  labor  is  of  the  prime  cost. 
c  The  prime  cost  is  of  the  gross  cost  of  goods. 
d  The  factory  overhead  is  of  the  prime  cost. 
e  The  total  manufacturing  expense  is  of  the  total 

gross  cost  of  goods.  . 

/  The  total  gross  cost  of  goods  is  of  the  selling 

price. 


386          WALSH'S  BUSINESS  ARITHMETIC 

13.  In    determining    the    factory    overhead    some 
manufacturers  include  a  share  of  the  administrative 
expense,     (a)  How  much  would  the  total  administra- 
tive and  selling  expenses,  etc.,  in  the  last  statement 
have  been  decreased  if  it  had  been  reduced  by  %  of 
the  administrative  expenses?     (6)  How  much  should 
be  the  factory  overhead  in  this  case? 

14.  What  would  be  the  net  profit  for  the  year  if 
5%  interest  on  the  capital  of  $50,000  were  deducted 
from  the  net  profit  shown  in  the  statement? 

15.  If   the   proprietor   had   allowed   himself   $3000 
per  year  for  his  services  what  would  then  have  been 
his  net  profit  after  deducting  also  the  interest  on  his 
capital? 

PROFIT  AND  Loss 

Mr.  Paulsen  in  1921  added  to  his  wares  a  new 
implement  which  he  sold  at  $8  each.  The  preceding 
year  his  sales  had  amounted  to  $50,000  with  a  profit 
of  $5000.  At  the  end  of  1921  his  receipts  were  $60,000, 
but  his  profits  had  fallen  to  $3000.  Upon  examining 
his  accounts  he  found  that  his  increase  in  receipts 
was  largely  due  to  sales  of  the  new  implement,  which 
he  then  ascertained  was  sold  by  other  manufacturers 
for  $10.50.  Careful  calculations  based  upon  the  bal- 
ance sheets  for  1920  and  1921  showed  that  the  imple- 
ment cost  him  $9.50  to  make  and  sell.  He  then  added 
to  his  books  a  series  of  cost  accounts  that  enabled  him 
to  avoid  future  mistakes  of  this  kind. 

16.  Complete  the  following  tables  giving  the  mate- 
rials required  for  a  dozen  shirt  waists  in  each  of  two 
factories.    (Give  results  in  mills.) 


FROM  PRODUCER  TO  CONSUMER         387 


Factory 

Yd. 

Price 

Material 

Trimmings 

Boxes 

Total 

Discount 

Net  total 

I 
II 

39 

38^ 

.66^ 
.66^ 

(a) 
(d) 

$1.130 

.870 

$.270 
.280 

(6) 

w 

$.563 
.915 

w 

(/) 

17.  Find  the  cost  of  a  dozen  of  each  of  the  fore- 
going, using  the  net  total  for  materials  obtained  in  the 
preceding  example: 


Factory 

Cost  of 
material 

Direct  labor 

Factory 
expense 

Selling 
expense 

Total  cost 

I 
II 

M 

(/) 

$.3980 
.5960 

$2.882 
3.536 

$5  .  195 
7.721 

(0) 
(*) 

18.  Each  of  the  above  lines  is  sold  to  retailers  at 
$42  a  dozen,  less  6%.  Find  the  gain  or  the  loss  a 
dozen  by  each  of  the  two  manufacturers. 


OVERHEAD  EXPENSES 

A  manufacturer  who  finds  that  his  factory  overhead 
in  1920  is  $45,000,  which  is  30%  of  the  prime  cost  of 
$150,000,  does  not  assume  in  fixing  1921  prices  that 
he  should  take  the  same  burden  rate  of  30%  without 
carefully  examining  into  all  the  conditions.  This 
examination  may  determine  his  selection  of  25%, 
or  possibly  35%.  How  nearly  right  has  been  his 
choice  can  be  determined  definitely  only  when  a  new 
balance  sheet  is  made  up,  which  may  not  be  until 
the  end  of  1921. 

19.  The  factory  expenses  of  the  Brown  Manu- 
facturing Company  comprise: 


388          WALSH'S  BUSINESS  ARITHMETIC 

Rent  of  factory  $7,500 

Power,  light,  and  heat  3,800 

Repairs  and  depreciation  600 

Fire  insurance  2,600 

Workmen's  compensation  100 

Taxes  1,100 

Superintendent,  timekeepers,  etc.  19,800 

Office  expenses  4,000 

Find  (a)  the  total  of  the  foregoing  factory  expenses. 

(6)  Find  the  total  of  the  following  selling  expenses : 
Rent  of  show  and  shipping  rooms  $3,400 

Salaries  of  office  force  6,100 

Salaries  and  commissions  of  salesmen         78,400 
Packing  materials  2,000 

Cartage  and  outward  freight  2,700 

Advertising  18,700 

Expense  of  collection  12,900 

Other  expenses  5,000 

20.   The  balance  sheet  of  a  small  factory  shows  net 
sales  amounting  to  $104,000,  and  expenses  as  follows: 
Raw  materials  $51,454 

Labor  32,665 

Factory  expenses  2,366 

Administration  3,430 

Selling  expenses  8,300 

Interest  on  loan  783 

Depreciation,  etc.  173 

(a)  Find  the  profit,  (b)  What  per  cent  is  realized  on 
the  capital  invested,  $50,000?  (c)  What  per  cent  of 
the  sales  is  the  profit? 


CHAPTER  FOUR 
THE  MERCHANTS'   PROBLEMS 

A  RETAIL  BUSINESS 

WRITTEN  EXERCISES 

1.  From  the  following  data  find  a  butcher's  profit 
during  the  year: 

Sales  for  the  year  $30,000 

3  salesmen,  $10,  $12.50,  $15  a  week.  $(a) 

Delivery  expense  900 

Rent  $390  Miscellaneous  $210  (b) 

Wrapping  $70  Advertising  $80  (c) 

Telephone  and  Postage  $90  Bad  debts  $210       (d) 

Office  boy  and  expenses  480 

Depreciation,  etc.  600 

Cost  of  goods  23,700           (e) 

Net  profit  (/) 

2.  The  net  profit  is  what  per  cent  (a)  of  the  yearly 
sales,    (b)  Of  the  cost  of  the  goods?     What  per  cent  of 
the  sales  are  (c)  the  salaries  of  the  salesmen;   (d)  the 
delivery  expenses;   (e)  the  rent;    (/)  the  miscellaneous 
expenses;    (g)  postage  and  bad  debts;    (h)  office  ex- 
penses;   (i}  depreciation,  etc.? 

3.  If   the   average   number   of   packages   delivered 
was  40  a  day  for  300  business  days,  (a)  what  was  the 
cost  of  delivery  for  each  package?     (b)  What  would  be 


390 


WALSH'S  BUSINESS  ARITHMETIC 


the  expense  of  delivery  at  3%  cents  a  package,  the 
rate  charged  by  a  newly  -organized  delivery  company? 
(c)  What  would  have  been  the  saving  last  year  by  the 
employment  of  this  company? 

4.   Find  the  total  yearly  expense  of  the  delivery 
company,  as  follows: 


Pay  roll  $16,548.72 

Feed  3,734.20 

Light  and  fuel  190.80 

Repairs  724.98 

Depreciation  325.  — 


Wagon  account  $210.— 

Shoeing  horses  708.35 

Harness  96.75 

Damage  claims  119.80 

Miscellaneous  930.40 


5.  (a)  From  the  foregoing  total  find  the  average  cost 
of  a  delivery,  786,300  deliveries  having  been  made  in 
the  year.     (6)  What  was  the  average  number  of  de- 
liveries a  day  for  the  300  business  days? 

6.  Find  (a)  to  (/)  the  total  daily  sales  of  shoe  sales- 
men as  follows,  (h)  to  (m)  the  weekly  sales  of  each, 
and  (g)  the  total  weekly  sales. 


Salesmen          Z 

Y 

X 

w 

V 

u 

Daily 
Total 

Monday               $42 
Tuesday                 38 
Wednesday            37 
Thursday               43 
Friday                    39 
Saturday                51 

$41 
36 
38 
40 
40 
50 

$40 
42 
33 
41 

42 
43 

$60 
57 
56 
58 
49 
65 

$55 
53 
56 
52 
53 
61 

$70 
69 
68 
72 
69 
83 

(a) 
(6) 
(c) 
(<0 

W 

(/) 

Total  for  week        (A) 

(0 

(;) 

(*) 

(0 

W 

(f) 

7.  Assuming  that  a  salesman's  weekly  pay  should 
be  8%%  of  his  net  sales,  find  the  value  of  the  weekly 
services  of  each  of  the  foregoing  to  the  nearest  dollar. 


FROM  PRODUCER  TO  CONSUMER 


391 


First  express  each  in  dollars  and  twelfths,  add  them,  and  compare  their 
sum  with  8%  %  of  (g).  If  the  results  agree,  the  rates  are  presumably  correct. 
Express  them  in  dollars,  as  called  for  by  the  problem. 

8.  Find  (a)  to  (I)  the  total  sales  a  month;  (ri)  to 
(s)  the  annual  sales  of  each,  and  (ra)  the  total  annual 
sales : 


Salesmen 

Z 

Y 

X 

W 

V 

U 

Monthly 
total 

January 

$887 

$775 

$840 

$1216 

$1095 

$1464 

(a) 

February 

863 

816 

785 

1235 

1208 

1593 

(*) 

March 

876 

839 

766 

1256 

1163 

1509 

M 

April 

904 

850 

808 

1265 

1084 

1477 

(d) 

May 

798 

905 

815 

1298 

1059 

1448 

U 

June 

875 

879 

825 

1289 

1158 

1527 

(/) 

July 

894 

864 

858 

1137 

1047 

1496 

® 

August 

856 

837 

798 

1206 

1053 

1544 

ft) 

September 

893 

823 

789 

1234 

1106 

1409 

(0 

October 

841 

787 

768 

1199 

1095 

1437 

0') 

November 

888 

748 

740 

1286 

1123 

1518 

(*) 

December 

863 

806 

829 

1275 

989 

1406 

(0 

Total  for  year 

(n) 

(o) 

(P) 

(4) 

(r) 

W 

c«) 

9.  (a)  Find  the  value  of  the  annual  services  of  each 
of  the  foregoing  to  the  nearest  dollar,  taking  8%%  of 
his  annual  sales  as  the  rate.     (6)  What  should  be  his 
weekly  pay  to  the  nearest  dollar,  taking  52  weeks  to 
the  year? 

Check  by  expressing  each  in  dollars  and  a  fraction, 
then  finding  their  sum,  etc. 

10.  A  butcher  slow  at  figures   and   not  having  a 
computing  scale,  makes  out  a  table  showing  the  charge 
to  be  made  for  fractions  of  a  pound  at  current  prices. 
He  expresses  results  in  cents,  considering  each  fraction 
of  a  cent  a  full  cent. 


392          WALSH'S  BUSINESS  ARITHMETIC 


Rates 

37^           21 

)t          27£          23            21ff 

3  oz. 

5   " 
7   " 
11    " 

l*t 

* 

13   ' 
Fill  out  the  foregoing  portion  of  the  table. 

NOTE:  In  sales  of  over  3  or  4  pounds  a  dealer  is  likely  to  reject  fractions 
of  a  cent  below  %. 

11.   The  balance  sheet  of  a  retail  shoe  store  shows  the 
receipts  and  the  expenditures  for  a  year  as  follows: 
Sales  during  the  year  $80,000 

Purchases  of  stock  $59,200 

Buying  expenses  $912 

Pay  of  salespeople  6800 

Advertising  1000 
Miscellaneous  selling  expenses       136 

Delivery  240 

Office  salaries  1400 

Office  supplies  160 

Rent  2640 

Heat  and  Light  480 

Insurance  304 

Taxes  296 

Repairs  96 

Depreciation  320 

Miscellaneous  expenses  136 

Bad  debts  80 

Total  expenses  (a) 

Total  outlay  (6) 

Net  profit  (c) 

Find   (a)   the  total  expenses  of  buying,  selling,  etc.; 

(6)  the  total  outlay,  including  cost  of  goods;    (c)  the 

net  profit. 


FROM  PRODUCER  TO  CONSUMER         393 

12.  A  furniture  dealer  who  found  that  on  sales  of 
$30,000  his  selling  expense  was  $7500,  fixed  the  price 
of  a  bedroom  set  by  adding  35%  to  its  cost  of  $60, 
believing  that  this  price  would  include  an  expense  of 
25%  and  a  profit  of  10%  on  it.     Find  (a)  the  selling 
price,     (b)  The  selling  expense  at  25%  of  the  selling 
price,     (c)  The  profit. 

13.  (a)  What  should  a  dealer  charge  for  a  range  that 
cost  him  $32.50  so  that  he  would  include  an  expense 
of  25  %  on  the  selling  price  and  a  profit  of  10  %  on  the 
same  price?     (6)  By  what  expense  should  he  increase 
$32.50? 

14.  The  following  shows  the  operating  expenses  of 
a  retail  shoe  store  for  a  year: 

Buying  expenses 

Freight  and  cartage  to  store  $600 

Selling  expense  (a) 

Pay  of  sales  force  $4,425 

Advertising  750 

Wrapping,  etc.  85 

Delivery  140 

Management  and  office  expense  1,100 

Fixed  charges  and  upkeep  (6) 

Rent  1,650 

Heat  and  light  300 

Insurance  190 

Taxes  200 

Repairs  and  renewals  60 

Depreciation  200 

Miscellaneous  expenses  and  bad  debts  800 

Total  expense  (c) 

Find  (a),  (6),  and  (c). 


394          WALSH'S  BUSINESS  ARITHMETIC 

15.  Find  the  net  profit  for  the  year  if  the  sales  are 
$50,000,  the  invoice  costs  are  $36,200,  and  the  total  ex- 
pense is  that  which  is  given  in  the  previous  example. 

16.  What  did  the  proprietor  pay  for  a  pair  of  shoes 
that  he  sold  for  $5,  if  he  made  the  rate  of  profit  shown 
by  the  figures  in  the  last  two  examples? 

17.  A  dry -goods  store  had  on  hand  at  the  beginning 
of  the  year  goods  that  cost  $4365.29.     There  were 
purchased    during    the    year    from    four    wholesalers 
goods  invoiced  at  $4234.56,  $5465.84,  $5798.77,  and 
$4867.58,  respectively.     There  were  on  hand  at  the 
end  of  the  year  goods  that  had  cost  $3757.83.     Find 
the  value  of  the  goods  sold. 

DEPRECIATION 

Gartland  &  Sons,  when  fixing  the  value  of  their 
goods  at  a  semi-annual  inventory,  make  an  arbitrary 
deduction  from  the  invoice  cost  according  to  the 
length  of  time  the  goods  had  been  in  stock,  a  5% 
deduction  being  made  for  goods  on  hand  at  two 
inventories  up  to  one  of  90%  for  those  on  hand  at 
seven  inventories. 

18.  The    following    statement    shows    the    invoice 
cost  of  goods  in  stock  at  the  present  inventory  arranged 
according  to  the  number  of  times  each  class  has  been 
inventoried.     It    shows    also    the    rate    of    deduction 
from  invoice  value  for  each  class. 

Find  the  present  value  of  each  class  (a  to  h),  the 
total  invoice  cost  (t),  the  total  inventory  (j),  and  the 
average  rate  of  deduction  (k). 


FROM  PRODUCER  TO  CONSUMER         395 


Times 
inventoried 

Invoice 
cost 

Rate  of 
deduction 

Present 
value 

1 

2 
3 
4 
5 
6 
7 
8 

$3856 
2430 
1884 
1060 
582 
365 
219 
87 

none 
5% 
10 
20 
33^ 
50 
90 
100 

(a) 
(b) 

u 

(d) 

14 

a) 
&) 

(K) 

Total  (t)  (k)  (j) 

To  obtain  (fc)  find  the  per  cent  the  difference  between  (i)  and  (j)  is 
of  (0. 

19.  A  druggist  spent  $2000  for  fixtures.  At  the  end 
of  the  year  he  deducted  20  %  of  their  cost  for  deterio- 
ration. The  next  year  he  deducted  20  %  of  their 
estimated  value  at  the  beginning  of  the  year.  This 
he  did  each  year  thereafter.  What  was  their  estimated 
value  at  the  end  of  the  eighth  year? 

SIGHT  EXERCISES 

1.  A  milk  dealer  delivers  200  quarts  of  milk  a  day. 
His  daily  expense  is  as  follows: 

Labor  $3.20 

Horse  feed  and  shoeing,  repairs,  etc.  1.30 

Depreciation  of  horses,  wagons,  etc.  .40 

Interest,  ice,  bad  bills,  insurance,  etc.  1.10 

(a)  Find  the  total  expense.  (b)  The  expense  a 
quart,  (c)  The  daily  profit  when  the  milk  costs  8  cents 
to  the  dealer  and  is  sold  for  16  cents,  (d)  What  per 
cent  of  the  gross  receipts  is  profit? 

2.  What  is  the  weight  of  200  quarts  of  milk  in  cans, 
the  milk  weighing  2  pounds  a  quart  and  an  empty  can 
of  10  gallons'  capacity  weighing  28  pounds? 


396          WALSH'S  BUSINESS  ARITHMETIC 
A  WHOLESALE  BUSINESS 

WRITTEN  EXERCISE 

The    balance   sheet    of   a    wholesale   grocer  shows 
receipts  and  expenditures  as  follows  for  a  year: 

$800,000 


Sales  during  the  year 

Cost  of  stock 

$ 

648,000 

Salary  of  buyer 

$2,500 

Other  expenses 

700 

Buying  expense 

(a) 

Salaries,  etc.,  of  salesmen 

18,400 

Advertising,  etc. 

1,600 

Selling  expense 

(b) 

Receiving  and  shipping 

9,280 

Packages  and  wrapping 

320 

Outward  freight,  etc. 

3,200 

Expense  of  handling 

(c) 

Salary  of  executive 

4,000 

Pay  of  clerks,  etc. 

5,600 

Postage,  etc. 

2,040 

Telephone  and  telegraph 

400 

Expense  of  collection 

560 

Other  expenses 

800 

Expense  of  management 

(d) 

Interest  on  loans 

12,000 

Rent 

3,200 

Heat  and  light 

400 

Taxes 

1,600 

Insurance 

900 

Repairs 

400 

Depreciation 

800 

Expense  of  upkeep 

(e) 

Miscellaneous  expenses 

900 

Bad  debts 

2,400 

Total  expenditures 


Find  the  net  profit  (/) 


CHAPTER  FIVE 

PARTNERSHIP 

WRITTEN  EXERCISES 

1.  A  and  B  entered  into  partnership,  A  contributing 
$4000  and  B   $5000.     Their  agreement  provided  that 
each  should  receive  from  the  profits  6  %  interest  on  his 
contribution   and   that   the   remaining  profits   should 
be  divided  equally.     If  the  business  showed  a  profit 
of  $4000  at  the  end  of  a  year,  what  should  each  receive 
as  his  share  including  interest  on  his  contribution? 

2.  West  &  Irwin,  fellow  clerks,  earning  $1500  and 
$1800,  respectively,  resigned  their  positions  and  formed 
a  partnership.     West  invested  $3500  and  Irwfn,  $2500, 
agreeing  to  share  profits  in  proportion  to  their  previous 
salaries,    after   first    receiving    6%    interest    on    their 
respective    investments.     What    should    each    receive 
as  his  share  of  a  profit  of  $5200  for  the  year,  including 
interest  on  his  capital? 


METHOD 

Profit  $5200 

Less  interest  due  West,  6  %  of  $3500  (a) 

"    Irwin,  6%  of    2500 (6) 

Remainder  to  be  divided       (c) 

:  receives  — 
15 

to  (a) 

1800 
1  reC6iveS  1500  +  1800  ( 

to  (6) 


West  receives  -  -  or  ~  of  (c),  in  addition 

1500  +  1800       11 


.  .  1800  6  . 

Irwin  receives  ,  „ , .    ,    ,..-  or  —  ot  (c),  in  addition 
15UU  +  loUU        II 


397 


398          WALSH'S  BUSINESS  ARITHMETIC 

3.  What    would   have   been    the   respective   shares 
of  West  and  Johnson  in  dividing  the  profit  given  in 
Example  2,  if  each  first  received  interest  on  his  invest- 
ment, then  the  amount  of  his  previous  salary,  and 
finally  one  half  of  the  remainder  of  the  profits? 

4.  What  profit  would  WTest  and  Johnson,  respec- 
tively, receive  if  the  entire  profits  in  Example  2  were 
divided  in  proportion  to  the  share  invested  by  each? 

5.  A  invested  $6000  in  a  business,  B,  $10,000,  and 
C,  his  services.     Out  of  the  profits  of  $7000,  C  was 
allowed  $1200  a  year,  and  each  of  the  others   10% 
of  the  sum  invested  by  him.     The  remainder  of  the 
profits  was  divided  equally  among  the  three;   find  the 
share  of  each. 

6.  What  would  be  the  share  of  each  in  Example  5 
if   C  received  $1200   a   year   and  15%   of   the  gross 
profits  of  $7000,  and  the  remainder  was  divided  be- 
tween A  and  B  in  proportion  to  their  respective  invest- 
ments? 

In  a  regular  partnership  to  which  the  members  contribute  different 
amounts,  the  profits  are  seldom  apportioned  in  proportion  to  the  respective 
sums  invested  when  each  partner  contributes  his  services  to  the  business. 

7.  The  business  of  Brown,  Jones  &  Company  was 
managed  by  Mr.  Thompson,  who  was  paid  for  -his 
services  a  salary  of  $3000  and   10%  of  the  profits. 
On  Jan.  1,   1920,   Brown's  investment  was  $30,000; 
Jones'  was  $20,000,  and  Smith's  (the  Co.),  was  $10,000. 
The  profits  of  the  year  after  the  deduction   of  all 
expenses,  including  the  salary  of  Mr.  Thompson,  but 
not   his   commission,    were   $20,000.     What   was   the 
share  of  each  partner? 


FROM  PRODUCER  TO  CONSUMER         399 

8.  A,  B,  and  C  engage  in  a  business  venture.  A  con- 
tributes $10,000  for  six  months  and  $10,000  additional 
for  the  next  six  months;  B  contributes  $30,000  for  four 
months  and  then  withdraws  $10,000,  leaving  $20,000 
for  the  next  eight  months.  C  contributes  $40,000  for 
the  year.  At  the  end  of  the  year  the  business  is  sold 
for  $100,000.  Give  the  sum  to  which  each  is  entitled 
on  the  basis  of  the  return  of  the  sum  he  had  in  the 
business  at  the  end  of  the  year,  and  a  share  of  the 
profit  in  proportion  to  his  average  investment. 


METHOD 

Received  for  business  $100,000 

A's  capital  at  end  of  year  20,000  ) 

B's       "        "     "     "     "  20,000  y  Deduct 

C's       "  40,000  j 

Profit  $20,000 

A's  contribution,       $10,000  for  6  mo.  =    $60,000  for  1  mo. 
20,000    "   6    "     =    120,000   "    1    " 

A's  aggregate  contribution  equals          =  $180,000  for  1  mo. 
B's  contribution,       $30,000  for  4  mo.  =  $120,000  for  1  mo. 

20,000   "   8    "     =    160,000   "    1 
B's  aggregate  contribution  equals  $280,000  for  1  mo. 

C's  contribution  of  $40,000  for  year  equals  $480,000  for  1  mo. 
The   sum  of  the  three  contributions  for  1  month  is 
$180,000  +  $280,000  +  $480,000,  or  $940,000 

180000       18        9 

A  s  fraction  of  this  total  is  -        -  or  —  or  - 

940000       94       47 

A's  share  is  $20,000  +  %7  of  $20,000 
B's     "      "     20,000  +  %  of       " 
C's     "      "     40,000  +  %  of       " 


400          WALSH'S  BUSINESS  ARITHMETIC 

9.   During  1921,  the  investments  of  the  members    of 
the  firm  of  Brown,  Jones  &  Co.  were  as  follows : 

Brown  Jones 

Jan.   1  invested  $30,000  Jan.    1  invested  $20,000 

May  1  added  10,000  Jun.    1  withdrew  5,000 

Aug.  1  withdrew  20,000  Sept.  1  withdrew  5,000 

Co.  (Smith) 

Jan.  1  invested  $10,000 
Jul.  1  added  10,000 
Oct.  1  added  10,000 

Find  the  average  investment  of  each  member  of  the 
firm  during  1921. 


METHOD 

Brown's  investment 

$30,000  for  4  months  (Jan.  to  May)  equals  $120,000  for  1  mo. 
40,000  "  3  "  (May  to  Aug.)  "  120,000"!  " 
20,000  "  5  "  (Aug.  to  Jan.)  "  100,000  "  1 

Aggregate  equals  $340,000  for  1  mo. 

%  of  which  is  Brown's  average  investment  for  the  year. 


10.  (a)  Find  the  ratio  the  average  investment  of  each 
member  of  the  firm  of  Brown,  Jones  &  Company 
bears  to  the  total  of  the  average  investments,  (b)  Find 
the  ratio  each  one's  aggregate  investment  bears  to  the 
sum  of  the  aggregates,  (c)  Find  the  capital  each 
member  has  in  the  business  at  the  end  of  the  year. 
If  the  entire  business  were  sold  at  the  end  of  the  year 
for  $75,000,  find  each  partner's  share  (d)  of  the  profit, 
(e)  of  the  sum  received  for  the  business. 


SECTION  VI 
FINANCING  BUSINESS 

CHAPTER  ONE 

REMITTING  MONEY 

A  boy  who  orders  a  rifle  from  a  dealer  in  a  distant 
city,  or  a  girl  who  writes  for  a  tennis  outfit,  may  send 
the  price  of  the  article  by  means  of  a  money  order,  ob- 
tainable at  any  money-order  post  office. 

DOMESTIC  MONEY  ORDER 

John  T.  Nicholson  of  Brainard,  Iowa,  sends  Marshall 
Field  &  Company,  Chicago,  a  postal  money  order  for 
four  dollars  and  a  half  for  a  pair  of  skates. 

He  fills  out  an  application  blank,  which  he  gives  to 
the  postmaster,  with  four  dollars  and  fifty  cents  and 
the  prescribed  fee. 

Fees  for  Domestic  Money  Orders 
For  orders  from  $0.01  to    $2.50  —  3^ 


( 

2.51 

a 

5. 

—  5i 

< 

5.01 

« 

10. 

-*i 

t 

10.01 

« 

20. 

-10* 

( 

20.01 

tt 

30. 

-  12^ 

t 

30.01 

« 

40. 

-  15f^ 

t 

40.01 

« 

50. 

-  18^ 

* 

50.01 

« 

60. 

-20^ 

( 

60.01 

« 

75. 

—  25^ 

t 

75.01 

<« 

100. 

—  30^ 

401 

402 


WALSH'S  BUSINESS  ARITHMETIC 


The  postmaster  fills  out  the  order  blank  shown  in 
the  accompanying  illustration.  He  retains  the  stub 
at  the  left  and  gives  Master  Nicholson  the  rest  of  the 
slip,  including  the  receipt  at  the  right,  which  the  latter 
detaches  and  retains,  mailing  the  remainder  to  Mar- 


:L-    [jjSiSSO  Bralna*  towt.  §72_ 

STUB    HH         United  States  Postal  Money  Order 


2..        972_ 


shall  Field  &  Company.     This  firm  collects  the  money 
by  depositing  the  order  in  its  bank. 

A  recipient  of  a  money  order,  who  has  no  bank 
account,  obtains  the  money  at  the  post  office  upon 
identification,  or  he  may  indorse  it  and  obtain  the 
money  from  a  merchant  who  knows  him. 

Telegraphic  Transfers  of  Money 

Mrs.  Aubrey  of  Seattle,  while  stopping  at  a  Pitts- 
burgh hotel,  finds  herself  in  need  of  funds.  She  tele- 
graphs to  her  husband  at  his  office  in  Seattle  to  send 
her  $300  by  telegraph.  He  gives  an  express  company 
the  order  to  make  the  transfer,  paying  $300,  with  the 
fee  and  the  cost  of  the  telegram  to  the  company's 
Seattle  agent.  The  express  company  delivers  the  cash 
to  Mrs.  Aubrey  at  her  Pittsburgh  hotel  in  less  than 
two  hours. 

The  following  are  the  rates  charged  by  the  express 
company  to  make  telegraphic  transfers: 


FINANCING  BUSINESS  403 

For  transfers  up  to  $50  —  $0.50 
For  transfers  over  $50  to  $75  —  0.60 
For  transfers  over  $75  to  $100  —  0.85 

For  each  additional  $100  up  to  $3000,  add  25^  to 
rate  for  $100.  For  each  additional  $100  over  $3000, 
add  20f£  to  rate  for  $3000. 


SIGHT  EXERCISES 

1.  Give  the  sum  paid  by  Mr.  Aubrey  to  the  express 
company,  including  90  cents  for  the  cost  of  the  tele- 
gram. 

2.  Give  the  sum  paid  to  the  express  company  to 
make  each  of  the  following  transfers,  adding  50  cents 
for  the  cost  of  the  telegram: 

a  $60  b  $70  c  $150  d  $1000  e  $3000 

/  $40  g  $90  h  $750  i  $2500  j   $5000 

A  telegraph  company  charges  85  cents  for  the  trans- 
fer of  $100  and  an  additional  charge  for  a  15-  word 
message. 

3.  Give  the  cost  of  a  15-word  message  when  the 
rate  is  50  cents  for  the  first  10  words  and  3  cents  for 
each   additional   word.     (This   is   generally   expressed 
as  50-3.) 

4.  Give  the  cost  of  a  15-  word  message  at  each  of  the 
following  rates: 

a  60-4  b  100-7  c  75-5  d  30-2 

e  25-2  f  125-8  g  35-2  h  40-3 

5.  Give  the  cost  of  each  of  the  following  messages  : 
Words       Rate          Words      Rate         Words      Rate 

13          60-4  25          75-5  16         35-2 

20         25-5  18         40-3  32         30-2 


404          WALSH'S  BUSINESS  ARITHMETIC 

BANK  DRAFTS 

J.  M.  Morse  of  Billings,  Oklahoma,  buys  a  motor 
truck  from  F.  B.  Lee  &  Company,  Joliet,  Illinois,  to 
be  delivered  on  the  cars  at  the  latter  place  on  receipt 
of  a  draft  for  $4000  on  a  Chicago  bank. 

Mr.  Morse  purchases  from  his  bank  the  following 
draft,  paying  15  cents  per  $1000  premium. 

A  Sight  Draft 


$4000  %o  Billings,  Oklahoma,  Nov.  5,  1919. 

At  sight  pay  to  the  order  of  F.  B.  Lee  &  Company 

Four  thousand  00/100 Dollars 

Value  received,  and  charge  to  the  account  of  The  Citizens  Bank. 
To  Commercial  National  Bank 

Chicago,  111.  R.  B.  Frazier 

Cashier 


Mr.  Morse  mails  this  draft  to  F.  B.  Lee  &  Company, 
who  ship  the  motor  truck.  His  check  would  not  be  so 
satisfactory  to  F.  B.  Lee  &  Company,  as  they  might 
have  to  pay  their  bank  the  expense  of  collecting  the 
money  from  the  Billings  bank.  In  the  case  of  the 
draft,  F.  B.  Lee  &  Company  receive  the  full  price  of 
the  truck,  Mr.  Morse  paying  the  Citizens  Bank  $4000.00 
for  the  draft. 

The  daily  papers  in  large  cities  give  the  rates  of 
exchange  on  drafts  bought  in  their  respective  cities. 
This  rate  is  sometimes  given  as  a  per  cent;  %%  pre- 
mium, %j%  discount,  etc.  When  it  is  stated  as  15 
cents  discount,  40  cents  premium,  it  means  the  rate 
per  $1000. 


FINANCING  BUSINESS  405 

A  draft  on  a  Billings  bank  bought  in  Chicago  might 
be  obtained  at  a  discount  of,  say,  10  cents  per  $1000. 

SIGHT  EXERCISES 

1.  Give  the  cost  of  a  sight  draft  for  $4000  when  the 
rate  is  15  cents  discount. 

$4000  -  4  X  I5i 

2.  Give  the  cost  of  each  of  the  following  sight  drafts: 
Face  Rate  Face  Rate 

a  $1000  10^  premium          b  $2000  %%  discount 

c     3000  15  ^discount  d    4000  %$%  premium 

e     5000  25 ^premium         /     6000  %%  discount 

The  foregoing  sight  draft  is  one  form  of  a  check 
drawn  by  the  Citizens  Bank  of  Billings  on  the  Com- 
mercial Bank  of  Chicago,  in  which  the  former  bank 
has  funds,  directing  the  latter  to  pay  to  the  order  of 
F.  B.  Lee  $4000. 

The  following  form  is  gradually  replacing  the  one 
given  above: 

A   CASHIER'S  CHECK 


The  Citizens  Bank 

Billings,  Oklahoma,  Nov.  5,  1919 
Commercial  National  Bank 

Chicago,  Illinois 
Pay  to  the  order  of  F.  B.  Lee  &  Company 

Four  Thousand  00/100 Dollars 

R.  B.  Frazier 

Cashier 


The  other  form  is  retained  for  drafts  payable  after 
sight.  For  the  employment  of  the  sight  draft  in  obtain- 
ing payment  for  grain,  etc.,  upon  delivery,  see  p.  362. 


406          WALSH'S  BUSINESS  ARITHMETIC 

Collections  by  Draft 

On  August  15,  1919,  the  Pacific  Fruit  Company, 
of  San  Francisco,  sold  to  Thos.  Appich  &  Sons,  Lincoln, 
Nebraska,  goods  to  the  amount  of  $987.50,  on  a  credit 
of  30  days.  The  latter  agreed  to  settle  on  Sep.  14 
by  paying  on  that  day  a  draft  drawn  upon  them  by 
the  sellers. 

A   Time  Draft 


ffi  987.50 


On  Sep.  8,  the  Pacific  Fruit  Company  draws  upon 
Thos.  Appich  &  Sons  by  making  out  the  foregoing 
draft,  which  it  deposits  in  its  bank,  the  Seaboard 
National.  This  bank  mails  it  for  collection  to  the 
National  Bank  of  Commerce,  at  Lincoln.  On  Sep.  11, 
a  messenger  from  the  latter  bank  presents  the  draft 
at  the  office  of  Thos.  Appich  &  Sons  for  acceptance. 
They  accept  it  by  writing  the  word  "Accepted"  across 
the  face  of  the  draft  with  the  date,  and  the  firm's 
signature.  On  Sep.  14,  three  days  after  the  accept- 
ance, Thos.  Appich  &  Sons  pay  the  money  and  receive 
the  draft.  The  National  Bank  of  Commerce  sends  its 
check  to  the  Seaboard  National  Bank,  and  the  latter 


FINANCING  BUSINESS  407 

credits   the   account   of   the   Pacific   Fruit   Company 
with  the  sum  received  less  the  expenses  of  collection. 

WRITTEN  EXERCISES 

1.  Make  a  copy  of  the  Pacific  Fruit  Company's 
three  days'  draft  on  Thos.  Appich  &  Sons. 

2.  On  the  back  write  the  "endorsement  for  col- 
lection" of  the  National  Bank  of  Commerce. 

3.  Across    the   face    write   Thos.  Appich    &    Sons' 
acceptance. 

4.  Write    Thos.    Appich    &    Sons'    check    on    the 
First  National  Bank  for  the  amount  of  the  draft. 

5.  Across  the  face  of  the  check  write  the  certification 
of  the  bank. 

In  the  foregoing  draft  the  Pacific  Fruit  Company 
is  called  the  drawer,  Thos.  Appich  &  Sons  are  called 
the  drawees,  and  the  Seaboard  National  Bank  is 
called  the  payee. 

If  Thos.  Appich  &  Sons  decline  to  accept  the  draft 
upon  presentation  by  the  National  Bank  of  Com- 
merce, the  latter  returns  it  to  the  Seaboard  National 
Bank,  which  notifies  the  drawer.  If  Thos.  Appich 
&  Sons  accept  the  draft,  and  fail  to  pay  the  amount 
at  its  maturity,  the  National  Bank  of  Commerce 
protests  the  draft  before  returning  it. 

Acceptance 

A  sight  draft  is  payable  upon  presentation,  except 
in  the  very  few  states  that  allow  three  days  of  grace. 

In  these  states  a  sight  draft  must  be  presented  for  acceptance.  When 
accepted,  it  is  payable  in  three  days  thereafter. 


408          WALSH'S  BUSINESS  ARITHMETIC 

A  time  draft  is  payable  at  the  specified  time  after 
acceptance.  To  "collect  from  Thos.  Appich  &  Sons 
the  amount  of  its  bill  on  Sep.  14,  and  to  give  them 
proper  notice,  the  seller  arranged  that  the  draft  would 
be  presented  for  acceptance  on  Sep.  11. 

In  arranging  with  Thos.  Appich  &  Sons  to  settle 
by  accepting  and  paying  a  draft,  the  seller  wished  to 
avoid  a  possible  delay  in  obtaining  its  money  through 
a  neglect  of  the  former  to  mail  their  check  on  time. 
It  felt  certain  that  they  would  not  be  likely  to  decline 
to  accept  and  pay  the  draft,  as  such  action  would 
tend  to  hurt  their  reputation  with  the  bank  that 
presented  the  draft. 

SIGHT  EXERCISES 

1.  Give  (a)  the  discount  on  the  foregoing  draft  at 
&%  of  $987.50.     (6)  The  proceeds. 

#%  of  $987.50         $4.9375 

Me%of  .6172  ^ofK% 

2.  Give  the  proceeds  of  each  of  the  following  notes 
discounted  at  6  %  on  the  day  it  is  drawn : 

Face  of  Note  Term  of  Discount  Face  of  Note  Term  of  Discount 

a  $450              60  days  6  $1200              15  days 

c     540              90  days  d    1320              30  days 

e     660              30  days  /     1800              45  days 

3.  Give  the  proceeds  of  each  of  the  following  drafts 
less  the  bank's  deduction: 

Face  of  Draft  Rate  of  Deduction  Face  of  Draft  Rate  of  Deduction 

a  $2400                %%  b  $1600                l%% 

c     1280                Y4%  d    3200                1%,% 

e     1680                %,%  /     2040               1%% 


FINANCING  BUSINESS 


409 


4.    Give   the  date  on  which  each  of  the  following 
drafts  becomes  due: 


Date  of 
Acceptance 

a  Aug.  15,  1921 
c  Feb.  10,  1920 
e  Dec.  23,  1921 


Number  of 
days  sight 

60 
30 
90 


Date  of 
Acceptance 

6  Jul.  29,  1919 
d  Mar.  16,  1920 
/  Feb.  23,  1921 


Number  of 
days  sight 

15 
40 
60 


TRADE  ACCEPTANCES 

A  manufacturer  with  moderate  capital  and  a  grow- 
ing business,  sometimes  finds  it  difficult  to  secure  from 
local  banks  loans  sufficiently  large  for  his  requirements. 
His  customers  pay  him  promptly  as  bills  become  due, 


I? 

I 

!iJ 


but  they  are  unwilling  to  take  advantage  of  his  offered 
deduction  for  cash  payment. 

By  means  of  the  Federal  Reserve  banks  which  will 
rediscount  commercial  paper  previously  discounted 
by  their  local  banks,  the  latter  are  enabled  to  make  safe 
loans  to  any  reasonable  extent,  especially  to  a  seller 
of  goods  offering  for  discount  paper  for  the  price  of 
these  goods,  made  by  the  purchaser  and  endorsed  by 
the  seller. 


410          WALSH'S  BUSINESS  ARITHMETIC 

The  preceding  type  of  draft,  a  trade  acceptance, 
shows  the  form. 

This  trade  acceptance  is  an  agreement  made  by 
Griffin  &  Stebbins  of  El  Reno,  Oklahoma,  to  pay  to 
Marc  F.  Valette  &  Company,  of  Galveston,  Texas, 
$787.40,  on  March  16,  1920,  for  goods  bought  on 
January  16,  1920.  The  draft  is  made  by  the  sellers 
on  the  day  the  goods  are  sold  and  is  immediately 
accepted  by  the  purchasers,  who  designate  their  bank 
as  the  place  of  payment. 

The  sellers  make  it  payable  to  "Ourselves"  so  that 
the  firm  name  will  appear  on  the  back  as  an  indorse- 
ment. 

The  form  differs  from  that  of  an  ordinary  time  draft 
by  the  statement  signed  by  Griffin  &  Stebbins  to  the 
effect  that  the  money  represents  a  debt  for  goods 
bought  by  them. 

Marc  F.  Vallette  &  Company's  bank,  the  Texas 
Guarantee  &  Trust  Company,  of  Galveston,  dis- 
counts this  acceptance  on  Jan.  18,  1920,  at  6%,  and 
places  the  proceeds  to  the  credit  of  Marc  F.  Vallette 
&  Company. 

On  Feb.  16,  this  bank,  needing  additional  funds  for 
loans,  rediscounts  the  acceptance  at  5  %  at  the  Federal 
Reserve  Bank  of  Dallas. 

Just  before  the  acceptance  becomes  due,  the  latter 
bank  sends  it  to  the  Citizen's  Bank  for  collection. 
The  latter,  on  Mar.  16,  charges  the  account  of  Griffin 
&  Stebbins  with  $787.40  (if  there  are  sufficient  funds 
to  their  credit)  and  sends  its  check  for  this  amount 
to  the  Federal  Reserve  Bank. 


FINANCING  BUSINESS  411 

In  discounting  this  acceptance,  each  bank  treats 
it  as  a  promissory  note. 

WRITTEN  EXERCISES 

1.  (a)  How  many  days  are  there  between  Jan.  18 
and  Mar.  16,  1920  (leap  year)?     Find  (6)  the  bank 
discount  at  6%  for  this  time  on  the  foregoing  trade 
acceptance,     (c)  The  proceeds. 

2.  (a)  For  how  many  days  did  the  Federal  Reserve 
Bank  discount  the  acceptance  (Feb.  16  to  Mar.  16)? 
(6)  What  did  it  deduct  from  the  face  of  the  accept- 
ance, for  this   term  at  5%?     (c)  Find  the  proceeds 
paid  to  the  Texas  Guarantee  &  Trust  Company. 

3.  (a)  How  much  did  this  bank  receive  from  Marc 
F.  Vallette  &  Company,  as  discount  on  the  acceptance? 

(b)  How  much  discount  did  it  pay  to  the  other  bank? 

(c)  Find  the  net  sum  received  by  it  as  interest  on  the 
acceptance,  for  the  time  it  held  the  latter  (Jan.  18  to 
Feb.  16). 

FOREIGN  TRANSFERS 

A  person  wishing  to  send  $100  or  less  to  a  son  in 
Europe  may  do  so  by  means  of  a  postal  money  order. 
A  large  sum  is  generally  transferred  by  a  banker's  bill 
(check)  or  by  a  bill  of  exchange.  The  amount  is  stated, 
as  a  rule,  in  the  money  of  the  country  to  which  the  bill 
is  sent. 

International  Money  Orders 

Domestic  rates  are  charged  on  a  money  order  made 
payable  to  a  U.  S.  soldier  in  any  military  camp,  to 
a  sailor  or  a  marine  on  any  U.  S.  vessel,  or  to  any 


412          WALSH'S  BUSINESS  ARITHMETIC 

person  in  Bermuda,  Canada,  Canal  Zone,  Mexico,  and 
many  islands  in  the  West  Indies.  The  Domestic 
forms  (p.  402)  are  used  for  these  orders. 

An  application  for  a  money  order  payable  in  other 
countries,  Austria,  Belgium,  Chile,  Denmark,  France, 
etc.,  for  example,  should  be  made  on  an  International 
form.  The  rates  are  as  follows: 


From  $0.01  to  $10  10^  From  $50.01  to  $60 

10.01  to    20  20j£  60.01  to    70 

20.01  to    30  30^  70.01  tt>    80          80^ 

30.01  to    40  40j£  80.01  to    90          90^ 

40.01  to    50  50j£  90.01  to  100    $1.00 

English  Money 

12  pence  (d.)  1  shilling  (s.) 

20  shillings  1  pound  sterling  (£) 

A  farthing  is  one  fourth  of  a  penny.     It  is  generally 
written  as  a  fraction. 

The  coin  value  of  £l  in  U.  S.  gold  is  $4.8665. 

WRITTEN  EXERCISES 

1.  (a)  Taking  the  value  of  £l  as  $4.87  what  sum  in 
U.  S.  money  will  pay  a  bill  in  Liverpool  amounting 
to  £9  5s.?     (6)  How  much  U.  S.  money  will  pay  for  a 
money  order  (including  fee)  to  settle  the  bill? 

2.  Find  the  sum  required  to  pay  for  a  money  order 
and  fee  to  settle  the  following  accounts  and  pay  the 
money  order  fee: 

a  Paris,  273.50  francs,  at  19.4  cents 
b  Brussels,  378.65  francs,  at  19.4  cents 
c  Madrid,  135.90  pesetas,  at  19.4  cents 


FINANCING  BUSINESS  413 

d  Rome,       463.75  lire,  at  19.4  cents 
e  Geneva,    312.60  francs,  at  19.4  cents 
/  Athens,     295.30  drachmas,  at  19.4  cents 

NOTE:  The  coin  value  of  each  of  these  units  is  19.3  cents,  the  extra  mill 
being  charged  to  cover  the  rate  of  exchange. 

Bills  of  Exchange 

Chas.  E.  Teale  &  Company  of  Peoria  wish  to  pay 
in  London  for  an  invoice  of  cloth  purchased  of  John 
M.  Stafford  amounting  to  £384  14s.  6d. 

They  purchase  the  following  sight  bill  of  exchange 
from  their  bank. 


£384  14s.  6d.  Peoria,  111.,  Dec.  9,  1920 

At  sight  of  this  original  bill  of  exchange   (duplicate  unpaid) 

pay  to  the  order  of  John  M.  Stafford 

Three  Hundred  Eighty-four  pounds,   fourteen  shillings,   six  pence 
Value  received,  and  charge  to  account  of 

To  Strachan  &  Rector  1  First  National  Bank 

London  Peoria,  111.,  U.  S.  A. 

England          )  per  Chas.  W.  Lyon 

Cashier 


The  bank  gives  Teale  &  Company  two  bills,  an 
original  and  a  duplicate,  marked  1  and  2,  respectively. 
They  send  the  former  to  Mr.  Stafford,  and  retain  the 
other  as  a  receipt,  sending  it  later  if  the  first  is  lost 
by  a  disaster  to  the  vessel  carrying  the  mail. 

The  cost  of  the  draft  depends  on  the  rate  of  exchange, 
which  varies  from  time  to  time.  The  daily  quotations 
give  the  cost  of  cable  transfers,  sight  bills,  and  sixty- 
day  bills. 

WRITTEN  EXERCISES 

1.  Chas.  E.  Teale  &  Company  pay  for  this  bill  of 
exchange  by  means  of  their  check  drawn  on  the  First 


414          WALSH'S  BUSINESS  ARITHMETIC 

National  Bank.     Find  the  face  of  the  check  at  the 
rate  of  $4.88^  a  £. 


ONE   METHOD 

Value  of  £250          $1221.25  %  of  $4885.- 

£125  610.625  %  of  £250 

£9  9  times  $4.885 

10s.  X  of  $4.885 

2s.  6d.  K  of  10s. 

2s. Xo  of  $4.885 

Value  of  £384  14s.  6d. 

Test  by  multiplying  $4.885  by  384.725  changing 
14s  6d.  to  the  decimal  of  a  pound.  Do  this  by 
subtracting  .115  times  384.725  from  5  times  384.725. 


2.  Find  the  cost  (a)  of  a  cable  transfer  to  Liverpool 
of  £178  16s.  9d.  at  $4.90  per  £  and  an  additional 
charge  of  $3.75  for  the  cable  message,  (b)  Of  a  60- 
day  bill  for  £236  9s.  4d.  at  $4.86%  a  £  sterling. 

A  Documentary  Bill  of  Exchange 

Arthur  Brown,  a  cutlery  manufacturer  of  Sheffield, 
England,  sells  Franklin  Bros,  of  Chicago  an  invoice 
of  goods  amounting  to  £265  7s.  8d.  including  in- 
surance on  the  goods  for  60  days.  He  consigns  the 
goods  to  the  buyers,  and  obtains  a  through  bill  of  lading 
to  Chicago,  the  freight  charges  to  be  paid  by  Franklin 
Bros. 

He  draws  a  sight  bill  on  Franklin  Bros,  for  the 
equivalent  of  the  foregoing  amount  in  U.  S.  money, 


FINANCING  BUSINESS  415 

to  which  bill  he  attaches  the  policy  of  insurance  and 
the  bill  of  lading.  These  combined  documents  con- 
stitute a  documentary  bill. 

Mr.  Brown  sells  this  documentary  bill  to  Hatton 
&  Hatton,  Sheffield  dealers  in  foreign  exchange. 
The  following  is  the  bill  itself: 


Sheffield,  England,  May  3,  1920 

At  sight  of  this  original  bill  of  exchange,  second  unpaid,  pay 
to  the  order  of  Hatton  &  Hatton 

Dollars 

Value  received,  and  charge  to  the  account  of 

To  Franklin  Bros.  Arthur  Brown 

Chicago,  111.,  U.  S.  A. 


He  assigns  to  Hatton  &  Hatton  the  bill  of  lading 
and  the  policy  of  insurance.  They  indorse  the  bill 
of  exchange  and  the  other  documents  to  their  Chicago 
correspondent,  and  send  to  the  latter,  for  collection, 
the  bill  with  the  other  papers. 

4.  (a)  How  much  does  Arthur  Brown  insert  in  the 
foregoing  bill  for  the  sum  to  be  collected  in  U.  S. 
money,  at  the  rate  of  $4.85%  a  £?     (6)  How  much 
does  he  receive  from  Hatton  &  Hatton  for  the  bill  of 
exchange,  at  the  rate  of  $4.84%  a  £? 

The  quotations  for  French  exchange  give  the  number 
of  francs  for  $1.  The  following  are  specimen  rates 
charged  in  St.  Louis  for  Paris  transfers: 

Cable  Transfers          Sight  Bills  60-day  Bills 

5.18%  @  5.17%       5.18%  @  5.18%        5.20%  @  5.20% 

5.  What  is  the  cost  a  franc  (a)  when  5.18%  francs 
is  obtained   for  a  dollar?     (6)  When  5.20%  francs  is 
obtained  for  a  dollar? 


416          WALSH'S  BUSINESS  ARITHMETIC 

6.  A  Paris  merchant  draws  a  60-day  bill  on  Oct.  5, 
1919,  on  a  Denver  creditor.     It  catches  a  mail  steamer 
sailing  4  days  later,  which  makes  the  voyage  in  6  days. 
Three  days  thereafter  it  reaches  the  drawee  who  then 
accepts  it.     The  latter  pays  it  on  maturity.     If  the 
proceeds  of  the  bill  require  the  same  time  for  their 
return  to  Paris  as  was  consumed  in  reaching  Denver, 
on  what  day  was  the  sum  received  by  the  drawer  of 
the  bill? 

The  quotations  for  German  exchange  give  the  value 
in  U.  S.  money  of  4  marks.  The  following  are  recent 
quotations : 

Cable  Transfers  Sight  Bills  60-day  Bills 

93%  @  94%  93%  @  93%  93%  @  93% 

7.  What  is  the  cost  of  a  cable  transfer  to  Hamburg 
of  1870.65  marks  at  94%  cents   for  4  marks,  and  a 
15- word  message  at  35  cents  a  word? 

8.  A  Berlin  merchant  sent  to  a  Seattle  purchaser 
an  invoice  amounting  to  2784.60  marks,  less  7%,  5, 
and  2%  %.     The  seller  added  the  freight  on  215  kilos  to 
Bremen  at  5.20  marks  a  kilo,  and  insurance  at  1  %  on 
the  net  cost  of  the  goods  and  the  freight  charge.     How 
much  must  the  purchaser  pay  for  a  sight  bill  at  93% 
cents  for  4  marks  to  cover  the  cost  of  the  goods  deliv- 
ered on  the  steamer  at  Bremen,  and  the  insurance? 


CHAPTER  TWO 
BANKS    AND    BANKING 

BANKS  OF  DEPOSIT  AND  DISCOUNT 

The  following  is  a  statement  of  the  condition  of 
the  Fairfax  National  Bank  at  the  close  of  business 
June  30,  1920: 


RESOURCES 

Bonds  and  Mortgages        $14,597. — 
Public  Securities  380,218.56 

Other  securities 
Loans 
Real  Estate 
Accrued  interest 
Due  on  acceptances 
Cash  on  hand  and  in  bank  438,906.68 
Total 


250,708.91 
1,411,007.25 
50,534.90 
14,501.14 
39,599.70 


(a) 


LIABILITIES 

Capital  stock  $125,000  — 

Surplus  150,000.— 

Undivided  profits  (ft) 

Deposits  2,257,933.56 

Reserved  for  taxes  4,626. — 

Accrued  interest  8,946. — 

Cashier's  checks  3,938.57 

Acceptances  39,599.70 

Total  (a) 


WRITTEN  EXERCISES 

1.  Find  the  total  resources  (a).     Insert  this  as  the 
total   of   the   liabilities   and  find    (6),   the   undivided 
profits. 

2.  Rewrite  the  foregoing  statement  of  resources  and 
liabilities,  expressing  the  items  in  thousands  of  dollars. 

First  write  the  totals  as  even  thousands.  Next,  add  the  thousands' 
column  of  the  resources  to  ascertain  how  much  must  be  carried  to  this 
column  to  make  the  new  total.  Then,  rewrite  the  items  as  thousands,  in- 
creasing by  1  thousand  the  necessary  number  of  items,  selecting  those 
having  the  largest  excess,  and  rejecting  the  remaining  figures  of  the  others. 

Thus,  write  "Bonds  and  Mortgages,  $15,000;  Public  Securities,  $380,000; 
Other  Securities,  $251,000;  etc. 

A  savings  bank  depositor  desiring  to  withdraw  any 
portion  of  his  funds  may  be  required  by  the  bank  to 
wait  60  days  for  his  money.  The  check  of  a  depositor 

417 


418          WALSH'S  BUSINESS  ARITHMETIC 

in  a  bank  of  deposit  (state  bank,  national  bank,  or 
trust  company)  must  be  paid  on  proper  presentation. 

Experience  has  shown  that  under  ordinary  conditions 
less  than  5  %  of  a  bank's  deposits  are  demanded  on  any 
one  day.  When  it  is  evident  that  larger  calls  for 
money  are  likely  to  be  made,  a  bank  can  withdraw 
some  of  its  deposits  in  other  banks,  sell  some  securities, 
rediscount  in  the  Federal  Reserve  Bank  some  accept- 
ances, collect  some  of  its  demand  loans,  etc. 

The  following  is  -a  condensed  form  of  a  collateral 
time  note: 

$24,000  %,  Butte,  Montana,  May  14,  1920 

On  Sep.    14,  1920,    for  value  received  we  promise  to  pay  to 
Merchants  &  Miners  Bank 


or  order,  at  its  banking  house 

Twenty-four     Thousand     00/100 Dollars 

with  interest  at  six  (6)  per  cent 

having  deposited   with   said   Bank,   as   collateral  security  for 
the  payment  of  this  liability,   the  following  property: 
Two  hundred  fifty  shares  of  stock  of  the  Pennsylvania 
Railroad  Company 

with  this  condition  that  the  Merchants  &  Miners  Bank  has  the  right  to 
call  for  such  additional  security  as  it  may  deem  proper,  and,  on  failure  to 
respond  forthwith  to  such  call,  this  obligation  shall  immediately  thereupon 
become  due  and  payable,  and  the  said  Bank  is  hereby  given  full  authority 
to  sell  and  deliver  the  whole  or  any  part  of  said  securities,  and  upon  such 
sale  the  said  Merchants  &  Miners  Bank  after  deducting  all  legal  costs  and 
expenses  may  apply  the  residue  to  pay  this  liability,  returning  the  over- 
plus to  the  undersigned.  And  the  undersigned  agrees  to  pay  the  holder 
hereof  any  deficiency  upon  demand. 

Wilcox  &  Wilcox 

LOANS  ON  COLLATERAL 

A  bank  is  always  willing  to  lend  money  to  the 
extent  of  at  least  80%  of  the  value  of  acceptable 
property  deposited  with  it  as  security.  To  be  accept- 
able, the  property  must  be  such  as  can  be  sold  by  the 
bank  at  once,  in  case  the  conditions  of  the  loan  are 


FINANCING  BUSINESS  419 

not  observed,  one  of  them  being  the  promise  of  the 
borrower  to  deposit  additional  security  at  the  call  of 
the  bank.  Bonds  or  stocks  are  generally  employed 
in  some  sections;  in  others,  warehouse  receipts  show- 
ing the  ownership  of  grain,  cotton,  etc. 

SIGHT  EXERCISES 

1.  (a)  Give  the  value  of  250  shares  of  stock  at  $132 
per  share.     (6)  What  is  80%  of  this  value? 

2.  When  a  bank  is  willing  to  lend  80%  of  the  value 
of  the  collateral,  how  much  of  the  latter  will  secure  a 
loan  of  $24,000? 

3.  For  how  many  days  is  the  foregoing  collateral 
note  drawn? 

4.  Give  the  discount  on  the  note  at  6  %. 

6.   Give  the  interest  at  6  %  (a)  on  $3000  for  30  days. 
(6)  On  $90,000  for  1  day.     (c)  On  $1  for  90,000  days. 

6.  Give  the  interest  at  6%  on  $1  for 

a  18,000  days     b  21,000  days     c  36,000  days     d  144  days 

7.  John  Martin  has  200  shares  of  stock  worth  $150 
a  share.     How  much  can  he  borrow  on  the  security 
of  this  stock  if  a  bank  will  loan  him  80  %  of  the  value? 

8.  (a)  To    borrow    $30,000,    what    should    be    the 
market  value  of  the  security?     (b)  How  many  bales  of 
cotton  at  $125  a  bale  would  equal  this  sum?     (c)  When 
corn  is  selling  at  $1.50  a  bushel,  a  warehouse  receipt 
for  how  many  bushels  would  be  required  as  security  for 
the  same  loan? 

INTEREST  PAYMENTS 

At    large    trade    centers    brokers    every    few    days 
borrow  money  payable  on  demand  with  interest.     At 


420 


WALSH'S  BUSINESS  ARITHMETIC 


the  end  of  each  month  the  bank  renders  a  statement 
of  the  interest  due  to  date  by  the  depositor,  and  noti- 
fies him  that  his  account  is  debited  with  the  total  in- 
terest items  due. 

INTEREST  STATEMENT 

Minneapolis,  Minn.,  Dec.  31,  1920 
THE  FLOUR  CITY  NATIONAL  BANK 
To  Jones  &  Cooke,  Dr. 

Your  account  has  been  debited  with  the  following  interest 
charges  to  date: 


1920 

Loans 

Days 

1  Day 

Rate 

Interest 

Dec. 

1 

$3000 

30 

$90,000 

6% 



5 

5000 

26 

130,000 



8 

7500 

23 

etc. 



12 

6000 

19 

etc. 



22 

12000 

9 

etc. 



27 

8000 

5 

etc. 



Totals 

(a) 

0) 

•  • 

(«) 

WRITTEN  EXERCISES 
1.   Find  the  interest  due  for  December,  1920. 


METHOD 

The  interest  on  $3000  for  30  days  is  the  same  as 
the  interest  on  $90,000  for  1  day;  on  $5000  for  26 
days,  it  is  the  same  as  that  on  $130,000  for  1  day. 

In  the  column  headed  "1  day"  write  the  product 
of  the  face  of  the  loan  by  the  number  of  days  for 
which  interest  is  due.  Obtain  (6)  the  sum  of  this 
column,  which  gives  the  number  of  dollars  on  which 
1  day's  interest  is  due. 

(b)  X  1  (da.)  X  .06 


FINANCING  BUSINESS  421 

2.  (a)  Find  the  total  amount,  principal,  and  interest, 
due  by  Jones  &  Cooke  to  the  Flour  City  National 
Bank  on  Dec.   31,   1920.     (b)  Find  the  total  of  the 
interest  if  the  rate  had  been  5  %. 

CHANGE  IN  RATE  OF  INTEREST 

As  the  demand  for  loans  increases,  the  interest  rate 
advances,  and  a  bank  may  "call"  a  demand  loan  un- 
less the  borrower  agrees  to  pay  a  higher  rate.  The 
following  example  shows  several  increases  during  a 
month. 

3.  Find  the  interest  charged  on  Oct.  31,  on  a  demand 
loan  of  $20,000,  the  rate  being  5%  from  Oct.  1  to 
Oct.  5,  inclusive;  5%%  from  Oct.  6  to  Oct.  10,  inclusive; 
5^%  from  Oct.  11  to  Oct.  20,  inclusive,  and  5%%  from 
Oct.  21  to  Oct.  31,  inclusive. 

BANK  TABLES 

The  large  amount  of  work  an  interest  clerk  is  called 
upon  to  do,  requires  the  employment  of  tables  to 
facilitate  his  calculations. 

The  following  is  a  portion  of  a  table  used  to  determine 
the  number  of  days  between  any  two  dates  in  a  year  of 
365  days.  An  extra  day  must  be  added  when  Feb.  29 
(leap  year)  falls  between  the  dates. 

To  find  the  time  between  any  day  in  January  and 
the  corresponding  day  in  another  month,  use  the 
January  line.  The  time  between  Jan.  13,  1921,  and 
Aug.  13,  1921,  is  212  days,  found  in  the  January  line 
and  the  August  column. 


422          WALSH'S  BUSINESS  ARITHMETIC 

DATE   TABLE 


Jan. 

Feb. 

Mar. 

Apr. 

May 

Jun. 

Jul. 

Aug. 

Sep. 

Oct. 

Nov. 

Dec. 

Jan. 

365 

31 

59 

90 

120 

151 

181 

212 

243 

273 

304 

334 

Feb. 

334 

365 

28 

59 

89 

120 

150 

181 

212 

242 

273 

Mar. 

306 

337 

365 

31 

61 

92 

122 

153 

184 

214 

Apr. 

275 

306 

334 

365 

30 

61 

91 

122 

153 

May 

245 

276 

304 

335 

365 

31 

61 

92 

Jun. 

214 

245 

273 

304 

334 

365 

30 

Jul. 

184 

215 

243 

274 

304 

335 

Aug. 

153 

184 

212 

243 

273 

Sep. 

122 

153 

181 

212 

Oct. 

92 

123 

151 

Nov. 

61 

92 

Dec. 

31 

The  time  between  Jan.  1  and  Aug.  13  is  224  days, 
12  days  more;  between  Jan.  13  and  Aug.  1  it  is  200 
days,  12  days  less;  between  Jan.  5,  1924,  and  Aug.  5, 
1924  (leap  year),  it  is  213  days. 

ORAL  EXERCISES 
1.   Find  the  time  between  the  following  dates : 

a  Jan.  5,  1921  and  Sep.  5,  1921 
c  Mar.  7,  1922  and  Jan.  8,  1923 
e  May  9,  1923  and  Mar.  9,  1924 
g  Aug.  8,  1924  and  May  1,  1925 
i  Oct.  6,  1925  and  Mar.  2,  1926 
k  Jul.  2,  1926  and  Jun.  7,  1927 


6  Feb.  13,  1922  and  Oct.  13,  1922 

d  Apr.  20,  1923  and  Sep.  15,  1923 

/  Jun.  25,  1924  and  Jan.  31,  1925 

h  Sep.  28,  1925  and  Apr.  20,  1926 

j  Nov.  30,  1926  and  Feb.  28,  1927 

/  Dec.  16,  1927  and  Jan.  31,  1928 


2.  Give  the  number  required  to  complete   (a)   the 
February  line;   (b)  the  February  column  in  the  Date 
Table. 

3.  (a)  How  many  days  does   each  number  in  the 
February  column  exceed  the  number  in  the  correspond- 
ing line  in  the  January  column?     (b)  How  many  days 
is  each  number  in  the  February  line  less  than  the 
corresponding  number  in  the  January  line? 


FINANCING  BUSINESS 


423 


4.   Give  the  numbers  required  to  complete  (a)  the 
successive  lines;   (b)  the  successive  columns. 


INTEREST  TABLES 

To  make  it  possible  for  a  clerk  to  determine  the 
interest  on  as  large  as  possible  a  number  of  accounts, 
banks  supply  books  showing  the  interest  for  1,  2,  3,  4, 
etc.,  to  360  days;  on  sums  of  $10,000,  $11,000,  $12,000, 
etc.,  to  $990,000;  at  each  of  the  customary  rates. 

The  following  is  an  extract  from  the  pages  showing 
the  interest  for  196  days,  on  a  small  number  of  prin- 
cipals, at  a  few  rates: 

196  days  —  Year  of  360  days 


Principal 

4% 

5% 

6% 

7% 

$1000 
2000 
3000 

$21.77,8 
43.55,6 
>^54.44,4 

$27.22,2 
54.44,4 
81.66,7 

$32.66,7 
65.33,3 
98. 

$38.11,1 
76.22,2 
114.33,3 

4000 
5000 
6000 

87.11,1 

108.88,9 
130  .  66,7 

108.88,9 
136.11,1 
163.33,3 

130.66,7 
163.33,3 
196. 

152.44,4 
190.55,6 
228.66,7 

7000 
8000 
9000 

152.44,4 
172.44,2 
196. 

190.55,6 
217.77,8 
245. 

228.66,7 
261.33,3 
294. 

266.77,8 
304.88,9 
343. 

SIGHT  EXERCISES 
1.   Give  to  the  nearest  cent  the  interest  on  each  of 


the  following  for  196  days: 


a  $10,000  at  4% 

e  20,000  at  5  % 

i  30,000  at  6% 

m  40,000  at  7  % 


6  $5000  at  6  % 
/  6000  at  7  % 
j  7000  at  5  % 
n  8000  at  4  % 


c  $900  at  4% 
g  800  at  5% 
k  700  at  6  % 
o  600  at  7  % 


d  $50  at  7% 

h  40  at  6  % 

/  30  at  5  % 

p  20  at  4  % 


424          WALSH'S  BUSINESS  ARITHMETIC 

2.   From  the  table,  give  the  interest  for  196  days, 
to  the  nearest  cent  on 

a  $1000  at  2  %        b  $2000  at  1%  %        c  $3000  at  3  %        d  $4000  at  3#  % 

NOTE:  The  bank  clerk  obtains  these  four  results  directly  from  his  book 
which  gives  interest  at  the  foregoing  rates:    2^%,  3}£%,  etc. 


WRITTEN  EXERCISES 

1.   Find  the  interest  for  196  days,  to  nearest  cent, 
on  $1234  at  4  %. 


METHOD 

Take  from  the  book  the  following  items,  at  4  % : 

Interest  at  4  %  on  $1000  —  $21.778 

200  4.3556  (&  of  $2000) 

30  .5444  (Xoo  of  $3000) 

"     "    "    4  .0871  (Mooo  of  $4000) 

"     "    "    $1234  ?  Ans. 

NOTE:  In  practice,  write  only  the  four  interest  items.    Check  by  finding 
the  interest  for  $617  and  multiplying  the  result  by  2. 


The  table  used  by  the  clerk  requires  but  two  items, 
that  for  $1200,  and  that  for  $34. 
2.    Find  the  interest  for  196  days  on 

a  $2345  at  4  %     b  $3456  at  5  %    c  $4567  at  6  %   d  $4567  at  7% 
e  9876  at  4%     /  8765  at  5%    g  7654  at  6%   h  6543  at  7% 

Check  each  result. 

ACCURATE  INTEREST 

In  England,  all  interest  is  calculated  on  the  basis 
of  365  days  to  the  year.  The  United  States  Govern- 
ment uses  the  same  basis,  as  do  banks  in  making  in- 
terest payments. 


FINANCING  BUSINESS 


425 


The  following  extract  shows  the  exact  interest  for 
264  days  on  a  few  sums,  at  specified  rates : 

264  days  —  Year  of  365  Days 


Principal 

4% 

5% 

6% 

7% 

$1000 

$36.16,4 

$43.39,7 

$50  .  63,0 

2000 

72  .  32,9 

86.79,5 

101.26,0 

3000 

108  .  49,3 

130.19,2 

151.89,0 

4000 

144  .  65,8 

173.58,9 

202.52, 

5000 

180  .  82,3 

216.98,6 

253.15, 

6000 

216.98,6 

260  .  38,4 

303.78, 

7000 

253.15,1 

303.78,1 

354.41, 

8000 

289.31,5 

347.17,8 

405.04, 

9000 

325.47,9 

390  .  57,5 

455.67,1 

WRITTEN  EXERCISES 
1.   Fill  out  the  4  %  column. 


Int.  on  $1000 


METHOD 

200 

X  264  X  .04 


m 

73 


$2112 
73 


Carry  out  the  quotient  to  five  decimal  places.  Mul- 
tiply this  successively  by  2,  3,  etc.,  to  9.  Write 
the  results  to  the  nearest  mill. 

Check  the  interest  on  $6000  and  $9000,  respectively, 
by  comparing  each  with  the  interest  on  $3000;  etc. 


2.   Find  the  interest  for  264  davs  on : 


a  $1234  at  5  % 
6  5678  at  6  % 


b  $2345  at  6  % 
/  6789  at  7% 


c  $3456  at  7% 
g  9876  at  5% 


d  $4567  at  5  % 
h  8765  at  6% 


426          WALSH'S  BUSINESS  ARITHMETIC 

CERTIFICATE  OF  DEPOSIT 

A  bank  that  pays  2  %  interest  on  a  customer's  daily 
balances  will  pay  3  %,  for  instance,  on  money  left  with 
it  for  3  months  or  more  on  a  special  deposit. 

John  T.  Collins  having  in  the  Mechanics  Bank  a 
balance  of  $3,800,  for  which  he  has  no  use  for  three 
months  or  more,  withdraws  $2500  from  his  account 
and  obtains  from  the  bank  the  following: 

Certificate  of  Deposit 


$2500%o  Woodrow,  Mont.,  fan.  25, 

MECHANICS  BANK 
This  certifies  that  fc>fw,  &.  &Mim* 
has  deposited  with  this  bank 

v&  Awyidi&d  00  /  fOO  ..............  Dollars 

payable  on  or  after  Apr.  25,  1920  to  the  order  of 


3          with  interest  at  3  per  cent  upon  the  return  of  this  certificate 
property  indorsed. 

faefih  tftzwoAt    /i/.  c&o*t6U'  l&e&k&i, 

Asst.  Cashier  Vice  Pres. 


3.   Find  the  exact  (accurate)  interest  on  the  fore- 
going certificate  from  Jan.  25,  1920,  to  Apr.  25,  1920. 


METHOD 

$2500  X  .03  X  91 
Find  the  interest  on 

91  days,  taking  365 

days  to  the  year.     Cancel  two  ciphers  in  $2500, 

and  the  decimal  point  in  .03.     Cancel  25  and  365. 


FINANCING  BUSINESS 


427 


4.  Mr.  Collins,  finding  he  needs  money  on  March  25, 
returns  the  certificate  on  this  date.  The  bank  allows 
him  but  2  %  interest  for  the  time  it  has  had  the  money. 
How  much  does  it  pay  Mr.  Collins,  principal  and 
exact  interest  at  2  %? 

INTEREST  ON  DAILY  BALANCES 

Some  banks  and  trust  companies  pay  interest  on 
daily  balances  when  these  are  in  excess  of  a  certain 
sum.  An  account  that  has  less  than  an  average 
balance  of  $200  is  probably  carried  by  a  bank  at  a  loss. 

The  following  table  shows  the  interest  for  1  day, 
taking  365  days  to  the  year: 

Interest  for  1  day  —  Year  of  365  days 


Principal 

2% 

2#% 

3% 

3^% 

$100,000 
200,000 
300,000 

$5.47,9 
10.95,9 
16.43,8 

$6.84,9 
13.69,9 
20.54,8 

$8.21,9 
16.43,8 
24.65,8 

$9.58,9 
19.17,8 
28.76,7 

400,000 
500,000 
600,000 

21.91,8 
27.39,7 
32.97,7 

27.39,7 
34.24,7 
41.09,6 

32.87,7 
41.09,6 
49.31,5 

.38.35,6 
47.94,5 
57.53,4 

700,000 
800,000 
900,000 

38.35,6 
43.83,6 
49.31,5 

47.94,5 
54.79,5 
61.64,4 

57.53,4 
65.75,3 
73.97,3 

67.12,3 
76.71,2 
86.30,1 

5.  A  depositor's  balance  for  20  days  is  $900;  for 
the  next  12  days  it  is  $1200;  for  the  next  15  days  it  is 
$1600.  Find  the  interest  at  2%  for  the  47  days. 


428          WALSH'S  BUSINESS  ARITHMETIC 


METHOD 

$900  for  20  days  =  $18,000  for  1  da. 
1200    "  12      "    =     14,400    "  1    " 
1600    "  15      "    =    24,000    "   1    " 
=  $56,400  for  1  da- 
To  find  the  interest  use  the  table 


6.   Find  the  exact  interest  on  the  following: 
a  $12,000  for  75  da.  at  2%         b  $3000  for  235  da.  at 
c  $14,000  for  61  da.  at  3  %         d  $4000  for  186  da.  at  3%  % 
e  $16,000  for  39  da.  at  2%        /   5000  for  127  da.  at 
g  $18,000  for  47  da.  at  3%        h   6000  for  206  da.  at 


SAVINGS  ACCOUNTS 
Postal  Savings  Certificates 

In  a  place  remote  from  banks,  a  person  ten  years 
of  age  or  over  can  obtain  interest  on  his  savings  by 
means  of  postal  savings  certificates,  obtained  through 
any  post  office. 

These  certificates  are  issued  in  denominations  of  $1, 
$2,  $5,  $10,  $20,  $50,  $100,  $200,  and  $500,  each 
bearing  the  name  of  the  depositor,  the  number  of  his 
account,  the  date  of  issue,  the  name  of  the  depository 
office,  and  the  date  on  which  interest  begins  (the 
first  day  of  the  month  next  following  the  day  on  which 
the  deposit  is  made). 

Interest  is  paid  at  the  end  of  a  full  year;  if  not 
collected,  it  accrues  annually.  No  interest  is  paid  on 
accrued  interest. 

If  a  certificate  is  lost  or  destroyed,  the  depositor 
may  obtain  a  new  one. 


FINANCING  BUSINESS 


429 


Postal  Savings  Bonds 

A  depositor  may  exchange  certificates  into  U.  S. 
postal  savings  bonds  on  Jan.  1  or  Jul.  1  by  making 
application  one  month  previously. 

These  bonds  are  issued  in  denominations  of  $20,  $100, 
and  $500.  They  bear  interest  at  2%%,  payable  semi- 
annually. 

SAVINGS  BANKS 

H.  M.  Devoe's  account  in  the  savings  department 
of  the  Mississippi  Valley  Trust  Company  shows 
deposits  and  withdrawals  as  follows: 


Date 

Deposits 

Interest 

Withdrawals 

Balances 

1921 

Jan. 

1 

327 

49 

Apr. 
May 

9 

8 

250 

75 

577 
502 

49 
49 

Jul. 
Sep. 

1 
10 

6 

54 

50 

509 
459 

03 
03 

Nov. 

4 

100 

559 

03 

1922 

Jan. 

1 

(a) 

(&) 

Mar. 

13 

75 

to 

May 

24 

150 

(d) 

Jul. 

1 

(•) 

(/) 

This  company  allows  interest  semiannual  ly  on 
January  1  and  July  1,  on  even  dollars  of  deposits  that 
have  been  in  the  bank  for  6  months  at  the  interest 
date. 

On  July  1,  1921,  2%  was  allowed  on  $327  (rejecting 
the  cents),  the  interest  being  added  to  the  balance. 
On  January  1,  1922,  2%  of  $509  was  allowed  (a); 
on  July  1,  1922,  2%  of  $559  was  allowed  (e). 


430          WALSH'S  BUSINESS  ARITHMETIC 

WRITTEN  EXERCISES 

1.  Write  from  the  book  the  answers  (a)  to  (/). 

2.  Copy   and   complete .  the  foregoing   account  by 
allowing    1  %    quarterly. 

Insert  two  other  interest  dates,  April  1  and  October  1. 
At  each  date  insert  1  %  of  the  smallest  sum  in  the 
bank  during  the  quarter. 

Other  banks,  while  allowing  interest  on  April  1  and 
October  1,  do  not  enter  interest  at  these  dates,  but 
add  it  to  the  interest  due  on  January  1  and  July  1, 
respectively. 

3.  Copy   and   complete   the  foregoing   account  by 
calculating  the  interest  due  on  April  1  and  October  1 
as  in  Example  2.     Do  not  credit  these  interest  items 
to  the  account  until  the  following  July  1  and  January 
1,  respectively. 

Calculate  the  interest  due  on  April  1,  but  do  not  enter  it  until  July  1, 
combining  it  then  with  the  interest  from  April  1  to  July  1.  This  makes  a 
slight  difference  in  some  of  the  "balances"  and,  therefore,  in  the  interest. 

4.  Copy   and   complete   the  foregoing   account  by 
allowing  interest  on  January  1  and  July  1,  at  the  rate 
of  4  %  annually  on  all  sums  three  months  in  the  bank 
at  those  dates. 

Check  up  the  interest  allowance  in  your  bank  book 
or  in  those  of  your  parents.  Read  carefully  the  in- 
terest rules  printed  on  one  of  the  cover  pages. 


CHAPTER  THREE 
STOCKS    AND    BONDS 

FORMING  A  CORPORATION 

Wishing  to  provide  employment  for  residents  of 
Accotink,  some  of  the  progressive  citizens  determined 
to  establish  a  cannery.  They  interested  the  farmers 
in  the  vicinity,  who  agreed  to  furnish  a  portion  of  the 
funds,  and  to  supply  fruits  and  vegetables  at  a  fair 
price. 

It  was  found  that  a  beginning  could  be  made  with 
$50,000,  and  a  charter  was  obtained  from  the  Legis- 
lature, authorizing  the  establishment  of  the  Accotink 
Canning  Company,  with  a  capital  of  $50,000. 


Capital  Stock  500  Shares  of 

$50,000  $100  each 

THE  ACCOTINK  CANNING  COMPANY 

Incorporated  1918 

Stock  Certificate  No.  #•#• 

This  certifices  that 

is  entitled  to  25  shares  of  $100  each  of  the  stock  of 

THE  ACCOTINK  CANNING  COMPANY 

fully  paid  and  non-assessable,  transferable  on  the  books  of  this 
corporation  only  by  the  holder  hereof  in  person  or  by  attorney  upon 
the  surrender  of  this  certificate. 

In  witness  whereof  this  corporation  has  caused  this  certi- 
ficate to  be  signed  by  its  duly  authorized  officers  and  to  be 
sealed  with  the  seal  of  the  Corporation,  this  ft/Ml  day  of 


Luoi 

Secretary  and  Treasurer  President 

431 


432          WALSH'S  BUSINESS  ARITHMETIC 

This  capital  stock  of  $50,000  was  divided  into  shares 
of  $100  each,  the  purchaser  of  one  or  more  shares 
receiving  a  stock  certificate  in  the  preceding  form. 

DIRECTORS  AND  OFFICERS 

The  stockholders  elected  twelve  (12)  directors  to 
serve  for  a  year  from  March  1,  1918.  To  this  Board 
of  Directors,  given  the  general  management  of  the 
corporation  and  the  selection  of  officers  to  take  charge 

of  the  details. 

PREPARATORY  EXERCISES 

1.  At  the  end  of  a  year,  the  profits  of  the  Accotink 
Canning  Company  were  found  to  be  $5510.85.     About 
what  per  cent  of  $50,000  does  this  represent? 

2.  The  directors  decided  to  distribute  $6  per  share 
among    the    stockholders,     (a)  How  much    was    thus 
distributed?     (b)  How  much  of  the  profits  remained 
for  working  capital,  etc.? 

3.  How  much  of  the  profits  did  Mr.  Laplace  receive, 
who  owned  45  shares? 

4.  Mr.  Laplace  sold  15  of  his  shares  to  Mr.  Beattys  at 
$140  a  share.     How  much  did  the  latter  pay  for  them? 

6.  At  the  end  of  the  next  year,  the  directors  dis- 
tributed $7  a  share.  What  per  cent  of  $140  did  Mr. 
Beattys  receive? 

PAR  VALUE  OF  STOCK 

By  the  par  value  of  a  stock  is  generally  meant  its 
cost  to  the  original  contributors  to  the  capital.  This 
is  generally  fixed  at  $100  a  share. 

The  par  value  of  a  share  of  the  Pennsylvania  Railroad  is  $50  a  share. 


FINANCING  BUSINESS  433 

When  the  stock  sells  below  its  par  value  ($100  in  the 
case  of  most  stocks),  it  is  said  to  be  sold  at  a  discount; 
when  it  sells  above  its  par  value,  it  is  said  to  be  sold 
at  a  premium. 

DIVIDENDS 

At  stated  times  the  directors  meet  to  declare  a 
dividend.  This  means  that  they  determine  the  sum 
per  share  to  be  paid  as  a  dividend  to  the  stockholders. 

In  the  case  of  the  Accotink  Canning  Company  for 
example,  the  books  showed  earnings  for  the  year  of 
$5510.85.  Of  this  amount  $1000  had  been  spent  for 
new  machinery,  and  $750  more  was  needed  for  the 
purpose.  To  have  funds  in  hand  for  emergencies,  same 
it  was  agreedto  distribute  $3000  among  the  stock- 
holders. This  made  the  dividend  $6  a  share. 

To  each  stockholder  of  record  was  mailed  a  check  for 
the  amount  of  his  dividend  at  the  rate  of  $6  for  each 
share  owned  by  him  according  to  the  Company's 
books. 

PRICES  OF  STOCKS 

The  daily  papers  give  the  prices  at  which  stocks 
are  bought  and  sold  at  the  Stock  Exchange.  The 
following  were  the  rates  for  a  few  stocks : 

Adams  Express  Co.         51%  American  Beet  Sugar    70% 

Baltimore  &  Ohio            57%  Delaware  &  Hudson    104% 

General  Electric            148%  Illinois  Central               96% 

Louisville  &  Nashville  116%  Union  Pacific                128% 

United  States  Steel        110%  Western  Union 


These  prices  mean  that  on  a  certain  day,  stock  of 


434          WALSH'S  BUSINESS  ARITHMETIC 

Adams  Express  Co.  sold  at  $51.25  a  share,  of  U.  S. 
Steel,  $110.1%  a  share,  etc. 

THE  STOCK  BROKER 

A  person  desiring  to  buy  or  tp  sell  stock  generally 
finds  it  advisable  to  do  so  through  a  stock  broker, 
who  charges  for  his  services  %%  of  the  par  value  of 
$100  a  share.  When  the  broker  buys  Baltimore  &  Ohio 
Railroad  stock  for  $57.75  a  share,  he  charges  his  client 
$57.87%,  adding  12%  cents  a  share  as  his  commission. 
When  he  sells  stock  of  the  General  Electric  Co.  for 
$148.37%  a  share,  he  remits  to  his  client  $148.25  a 
share,  deducting  his  commission  of  12%  cents  a  share. 

NOTE:  In  all  examples  in  stocks  take  as  the  par  value  $100  unless  another 
value  is  given. 

SIGHT  EXERCISES 

1.  A  broker  bought  for  a  client  stocks  for  which  he 
paid  the  following  prices: 

a  70%  b  83%  c  97%  d  101%  e  93 

/  56%  g  64%  h  73%  i   174%  j  86% 

Give  the  cost  of  each  per  share  to  the  client,  after  he 
pays  the  broker's  commission  of  %  %. 

2.  Stock  was  sold  through  a  broker  at  the  following 
rates : 

a  68  b  75%  c  86%  d  97%  e  118% 

/  57%  g  82%  h  95%  i  88%  j  129 

Give  the  price  per  share  received  by  the  seller  in  each 
case,  after  the  deduction  of  the  broker's  commission 


FINANCING  BUSINESS  435 

3.  A    broker    filled    orders    for    stocks,  buying   the 
following  quantities  at  the  prices  specified: 

a  25  shares  at  83%  b  4  shares  at  71% 

c  88  shares  at  99%  d  6  shares  at  60% 

e  50  shares  at  80%  /  8  shares  at  87% 

Give  the  cost  of  each  lot  when  %%  commission  is 
added  to  each  purchase. 

4.  Give  the  price  received  by  the  seller  of  each  of 
the  following  lots,  after  the  deduction  of  the  broker's 
commission  of  %  % : 

a  25  shares  at  127%  b  4  shares  at  81% 

c  96  shares  at  100  d  6  shares  at  70% 

e  50  shares  at  144%  /  8  shares  at  62% 

6.  How  much  commission  does  a  broker  receive 
who  sells  25  shares  at  127%,  and  96  shares  at  100? 

Ignore  the  prices,  since  a  broker's  commission  is  the  same  whether  he 
sells  a  $100  share  for  $27%  or  for  $127%. 

WRITTEN  EXERCISES 

1.  A  broker  bought  for  a  customer  176  shares  of 
General  Electric  at  148%.  How  much  did  the  stock 
cost  the  latter  including  the  broker's  commission? 


METHOD 

The   stock   cost   the   cus-  100  sh.  $14,862.50 

tomer  $148.62%  a  share,  in-  50    "  7,431.25 

eluding  commission.    Find  25    '  3,715.625 

the  product  of  176  times  1    "  148.625 

$148.62%  by  aliquot  parts.  Ans.  $16,158.— 
Test   by   multiplying    176 
by  148%. 


436          WALSH'S  BUSINESS  ARITHMETIC 

2.  Find  the  amount  a  purchaser  should  pay  for 
each  of  the  following  blocks  of  stock,  adding  a  com- 
mission of  %%  to  the  given  rates: 

a  125  shares  at  163%  b  75  shares  at  57% 

c  287  shares  at  148%  d  63  shares  at  64% 

e  144  shares  at  126%  /  98  shares  at  76% 

3.  A   broker   sold   for   Mr.   Jenkins   275   shares   of 
Illinois    Central    at    96%.     How    much    should    Mr. 
Jenkins  receive  after  the  deduction  of  the  commission? 


METHOD 

Mr.  Jenkins  receives    250    shares  @  $96.75  $24187.50 

$96%  -  $%  a  share,      _25  2418.75 

or  $96.75.     Test       £75        «       «        "    Ans.  $26606.25 


4.  Find  the  sum  due  each  seller  of  the  following 
blocks  of  stock  after  deduction  of  the  broker's  commis- 
sion, the  respective  quantities  and  selling  prices  being 

a  216  shares  at  112%  6  86  shares  at  76% 

c  154  shares  at  106%  d  79  shares  at  59% 

e  375  shares  at  184%  /  38  shares  at  64% 

5.  M.  E.  Kelley  sent  his  broker  $10,000  with  in- 
structions to  buy  stock  of  the  Pacific  Lumber  Co. 
How  many  shares  at  86%  could  be  bought,  and  how 
much  money  should  the  broker  return  his  principal 
after  deducting  his  commission  at  %%? 

6.  Find  the  maximum  number  of  shares  at  each  of 
the  following  rates  that  can  be  bought  for  $10,000,  and 
the  balance  remaining  after  paying  for  the  shares  and 
the  commission  of  %  %. 

a  94%  b  86%  c  74%  d  116%  e  127 


FINANCING  BUSINESS  437 

7.  Mr.  Guiry  ordered  his  broker  to  sell  a  sufficient 
number  of  shares  of  Midvale  Trolley  Co.  to  realize 
$10,000  after  the  deduction  of  the  usual  commission. 
How  many  shares  at  114%  must  be  sold? 


METHOD 


$10,000  -i-  $114%  =  40,000  -T-  459  =  87 
Ans.  88  shares. 


8.  Find  the  number  of  shares  of  each  of  the  following 
that  must  be  sold  to  realize  $10,000. 

a  96^  b  87%  c  64%  d  109%  e  137% 

PREFERRED  STOCK 

In  1921,  needing  more  money  to  extend  the  business 
of  the  Accotink  Canning  Company,  its  stockholders 
authorized  the  issue  of  500  shares  of  preferred  stock,  on 
which  an  annual  dividend  of  $6  a  share  was  to  be  paid 
before  any  dividend  payment  was  made  to  holders  of 
the  original  (common)  stock.  Each  stockholder  was 
permitted  to  buy  for  $100  each  the  same  number  of 
shares  as  he  held  of  the  common  stock.  Owners  of 
the  latter  unable  or  unwilling  to  buy  preferred  stock 
could  sell  their  rights. 

SIGHT  EXERCISES 

1.  (a)  How  much  should  an  outsider  pay  for  6  %  pre- 
ferred stock  to  enable  him  to  obtain  5%  annually 
on  his  investment? 

-v- ?=5% 


438          WALSH'S  BUSINESS  ARITHMETIC 

(6)  How  much  a  share  could  he  afford  to  pay  for  the 
right  to  purchase  the  preferred  stock? 

2.  If  the  company's  profits  the  next  year  were  $9000, 
how  much  would  be  left  after  paying  the  holders  of 
500  shares  of  preferred  stock  $6  a  share  and  the  holders 
of  500  shares  of  common  stock  $7  a  share? 

3.  The  folio  whig  year  the  amount  available  for  the 
payment  of  dividends  was  only  $5750.     (a)  How  much 
would  remain  for  the  holders  of  common  stock  after 
the  payment  of  $6  a  share  to  the  holders  of  the  pre- 
ferred stock?     (6)  How  many  dollars  a  share  could  be 
paid  the  former? 

BONDS 

Finding  that  it  could  use  to  advantage  a  large  sum 
of  money,  the  Accotink  Canning  Company  offered  for 
sale  bonds  maturing  in  20  years,  to  the  amount  of 
$50,000,  bearing  interest  at  5  %  a  year,  payable  semi- 
annually. 

As  security  the  company  mortgaged  its  property, 
worth  $80,000,  to  the  Old  Dominion  Trust  Company 
for  the  benefit  of  the  bondholders. 

The  bonds  were  issued  in  denominations  of  $100, 

$500,  and  $1000. 

SIGHT  EXERCISES 

1.  How  much  will  be  required  annually  to  pay  6% 
on   bonds    amounting    to    $50,000,  C%  dividends    on 
preferred    stock   of    $50,000,    and    7%    dividends    on 
common  stock  of  $50,000? 

2.  In  order  to  pay  the  principal  of  $50,000  in  20 
years,   how  much   must  a  company   set  aside  semi- 
annually  out  of  its  gross  profits? 


FINANCING  BUSINESS  439 

3.  How  much  must  it  set  aside  semiannually  to 
allow  for  2  %  annual  depreciation  on  equipment  valued 
at  $43,750? 

PUBLIC  SECURITIES 

Bonds  are  issued  to  raise  money  to  build  schools, 
improve  roads,  install  water  systems,  etc.,  etc. 

Investors  can  be  certain  that  the  interest  on  these 
bonds  will  be  paid  as  it  becomes  due,  and  the  principal 
at  the  time  the  bond  matures. 

As  the  benefits  from  the  foregoing  improvements 
will  continue  for  some  time  it  is  only  fair  that  the 
payment  of  the  cost  thereof  should  be  spread  over  a 
series  of  years. 

INTEREST  PAYMENTS 

An  examination  of  a  Liberty  Bond  will  show  that  it 
specifies  the  principal,  the  rate  of  interest,  the  time  of 
each  interest  payment,  and  the  date  when  the  principal 
is  payable. 

Bonds  are  issued  in  two  forms,  registered  and 
coupon.  The  registered  bond  shows  the  name  of  the 
owner.  His  address  is  kept  by  the  Treasury  Depart- 
ment, and  the  check  for  the  interest  is  mailed  to  him. 
If  he  wishes  to  sell  the  bond  he  transfers  it  by  assign- 
ment, which  must  be  recorded  by  the  Washington 
authorities,  so  that  they  may  send  interest  checks 
to  the  new  owner. 

One  advantage  of  the  registered  bond  is  that  the 
owner  suffers  no  financial  loss  if  it  is  destroyed  or 
stolen.  A  disadvantage  to  a  person  desiring  to  obtain 
cash  at  once,  is  the  necessity  of  waiting  a  few  days  for 
the  intending  purchaser  to  obtain  title. 


440          WALSH'S  BUSINESS  ARITHMETIC 

COUPON  BONDS 

A  coupon  bond  is  generally  payable  to  the  holder, 
making  it  possible  to  sell  it  by  handing  it  over  to  the 
purchaser. 

A  20-year  bond  with  interest  payable  semiannually 
contains  as  a  part  of  it  40  interest  coupons,  one  of  which 
is  detached  each  half  year.  They  are  numbered  from 
1  to  40;  each  shows  the  amount  of  the  half-yearly 
interest  and  the  date  when  it  is  due.  When  this  day 
arrives  the  holder  of  the  bond  detaches  the  current 
coupon  and  cashes  it  through  his  bank. 

DENOMINATIONS 

Bonds,  registered  and  coupon,  are  issued  in  various 
denominations:  $50,  $100,  $500,  $1000,  $5000,  $10,000, 
etc. 

BOND  QUOTATIONS 

Wlien  the  price  of  a  bond  is  given  as  115,  this  means 
115%  of  the  face  of  the  bond.  If  bought  or  sold 
through  a  broker,  there  is  a  charge  of  %%. 

A  bond  quotation  gives  the  rate  payable  for  a  bond 
bought  on  an  interest  day.  If  bought  thereafter, 
the  buyer  pays  the  "accrued"  interest;  that  is,  the 
interest  earned  by  a  bond  from  the  day  the  last  interest 
was  paid  until  the  day  of  purchase. 

ACCRUED  INTEREST 

When  a  person  on  Aug.  15  sells  a  bond  paying  in- 
terest on  Jan.  1  and  Jul.  1,  he  is  entitled  to  the  interest 
it  has  earned  during  these  45  days  between  Jul.  1  and 


FINANCING  BUSINESS  441 

Aug.  15.  He  turns  the  bond  over  to  the  buyer  with 
the  coupon  covering  six  months'  interest  from  Jul.  1. 
If  the  bond  purchased  is  a  4  %  one  for  $1000  and  the 
price  is  115,  the  purchaser  pays  $1151.25+45  days' 
interest  on  $1000  at  4  %. 

In  the  following  examples  take  the  interest  for  the 
accrued  time,  at  the  rate  paid  by  the  bond,  on  the 
basis  of  360  days  to  the  year. 

The  pupil  should,  however,  know  that  in  large  transactions  the  buyer 
may  insist  upon  actual  interest,  365  days  to  the  year.  The  most  equitable 
way  is  to  take  the  number  of  days  in  the  interest  period  and  to  calculate 
the  accrued  interest  on  the  basis  of  the  number  of  days  in  this  period. 

WRITTEN  EXERCISES 

1.  At  112%  plus  brokerage,  find  the  cost  of  bonds 
to  the  amount  of  $15,000,  bearing  interest  at  the  rate 
of  5%,  payable  semiannually  on  March  1  and  Sep- 
tember 1,  when  the  purchase  is  made  (a)  June  20, 
(6)  September  6. 


METHOD 

(a)  Accrued  interest  on  $15,000,  Mar.  1  to  Jun.  20, 
111  da.  at  5%  is  $231.25 

(b)  For  5  da.  at  5  %,  it  is  $10.42. 

The  cost  of  the  bonds  on  Mar.  1  or  on  Sep.  1  after 
the  removal  of  the  proper  coupon,  would  be 
times  $15,000  or  $16,837.50 
Total  cost  (a)  $16,837.50  +  $231.25  =  Ans. 
Total  cost  (b)     16,837.50  +      10.42  =  Ans. 


2.  Find  the  amount  paid  for  each  of  the  following 
purchases  of  bonds.  Add  brokerage  to  the  given 
price. 


442          WALSH'S  BUSINESS  ARITHMETIC 

Bought  Price  Face  Val.  Int.  rate  Int.  payable 

a  Jun.   28  112^  $15,000       6%            Jan.    1 

6  Sep.    20  97%  12,000  3%            Jul.     1 

c  Nov.  19  104K  20,000  5%            Oct.    1 

d  Dec.  13  96%  18,000  3%            Dec.  1 

e  May  12  101%  24,000  4  %            Mar.  1 

INCOME  RATE  ON  INVESTMENTS 

When  a  person  buys  a  3%  bond  for  90,  including 
brokerage,  and  holds  it  until  its  maturity,  5  years  later, 
his  total  income  from  a  $100  bond  would  be  $15  for 
5  years'  interest  plus  $10,  the  difference  between  $90, 
the  cost  of  the  bond,  and  the  $100  he  received  for  it 
when  it  was  paid  off. 

This  total  income  of  $25  in  5  years  represents  an 
average  of  $5  a  year,  which  was  obtained  from  an 
investment  of  $90,  making  the  annual  rate  5%  %. 

These  figures  ignore  the  interest  obtained  by  the 
reinvestment  of  each  interest  item  as  it  is  collected. 
Large  investors  take  this  into  account,  also  the  fact 
that  the  interest  is  payable  quarterly,  semiannually, 
or  annually.  They  ascertain  the  income  rates  from 
bond  tables,  which  involve  calculations  that  can  be 
made  only  by  experts. 

SIGHT  EXERCISES 

1.  Ignoring  the  matte?  of  interest  on  interest,  how 
much  less  than  $100  must  a  buyer  pay  for  a  3%  bond 
to  receive  $4  profit  a  year  when  the  bond  matures  in 
(a)  1  year;    (b)  2  years;    (c)  3  years? 

2.  How  much  more  than  $100  can  a  buyer  pay  for 
a  5%  bond  maturing  in  (a)  1  year;    (6)  2  years;   (c)  3 
years? 


CHAPTER  FOUR 
FINANCING   THE    GOVERNMENT 

THE  TAXPAYER 

Everybody  contributes  to  the  expenses  of  running 
the  government.  He  may  not  receive  a  bill,  but  he 
pays  taxes  when  he  buys  anything  the  price  of  which 
includes  a  tax  paid  by  someone  else.  If  he  is  not  the 
owner  of  a  house,  a  portion  of  his  rent  is  used  by  his 
landlord  to  pay  the  tax.  Everybody,  therefore, 
should  be  interested  in  the  proper  use  of  government 
receipts. 

THE  BUDGET 

The  residents  of  a  rural  school  district  meet  annually 
to  determine  the  sum  to  be  raised  for  educational 
purposes. 

The  legislative  department  of  a  county,  a  city,  or 
a  state  fixes  the  sums  to  be  raised  for  its  special  pur- 
poses. Each  body  receives  estimates  from  the  officers 
in  charge  of  the  various  activities,  and  finally  deter- 
mines the  sum  to  be  raised  by  taxation. 

% 

STATE  REVENUES 

WRITTEN  EXERCISES 

1.  Using  the  following  data,  write  from  the  book 
the  total  of  a  state's  revenues. 

443 


444          WALSH'S  BUSINESS  ARITHMETIC 

Direct  Taxes  $45,510.43 

Indirect  Taxes 

Excise  114,787.50 

Corporations  5,894,051.60 

Inheritance  1,280,660.49 

Stock  transfers  985,902.38 

Secured  debt  635,902.53 

Mortgages  745,132.12 

Motor  vehicles  262,747.— 

Other  revenue  receipts  643,982.05 

Total  $ 

2.  The  direct  taxes  are  collected  from  the  counties. 
What  per  cent  of  the  revenue  is  obtained  in  this  way? 

3.  Write  the  total  of  the  following  yearly 

EXPENDITURES  OF  A  STATE 

Executive  $18,798.80  Defensive  $108,490.76 

Administrative  250,244.41  Penal  111,178.29 

Legislative  153,004.94  Curative  687,904.95 

Judicial  200,755.71  Charitable  322,434.56 

Regulative  382,962.83  Protective  160,371.90 

Educational  250,249.90  Constructive  201,494.44 

Agricultural  224,516.88  General  78,596.88 

THE  CITY  BUDGET 

The  following  are  the  approximate  appropriations 
made  by  the  city  of  Belle  Haven  for  the  year  1921 : 

Department  of  Finance  $43,420 

Department  of  Water  and  Sewers  39,380 

Department  of  Public  Works  42,450 

Department  of  Buildings  10,800 

Department  of  Charities  and  Correction  32,650 

Department  of  Police  35,400 

Fire  Department  31,250 


FINANCING  BUSINESS  445 

Department  of  Parks  24,000 

Department  of  Health  12,250 

Judicial  Purposes  10,000 

Department  of  Street  Cleaning  11,350 

Interest  on  City  Debt  44,500 

Sinking  Fund  24,000 

Expenses  of  Administration  48,000 

Department  of  Education  90,450 

Sundry  Expenses  8,450 

4.  Write  the  total  appropriations  for  the  year. 

5.  Find   the   per   cent   of   the   total    appropriation 
allowed  for   (a)  Educational  purposes,     (b)   Charities 
and    Correction,     (c)    Fire    department,     (d)    Police 
purposes,     (e)   Parks.     (/)   Health,     (g)   Interest  and 
Sinking  Fund. 

VALUATIONS 

For  purposes  of  taxation,  the  value  of  the  property 
in  the  city  is  fixed  by  officials  called  assessors.  They 
visit  each  parcel  once  a  year;  they  are  furnished  with 
maps  of  every  block,  showing  the  character  of  the 
improvements;  and  they  endeavor  in  every  way  to 
keep  acquainted  with  the  changes  in  the  value  of  the 
real  property  during  the  year.  They  then  fix  the 
assessed  value,  which  is  sometimes  as  low  as  one  half 
its  actual  value. 

Personal  property  is  also  assessed,  and  its  valuation  is 
added  to  that  of  the  real  estate,  the  sum  of  both  repre- 
senting the  total  valuation  for  purposes  of  taxation. 

SIGHT  EXERCISES 

1.  (a)  When  property  worth  400  millions  of  dollars 
is  valued  by  the  assessors  at  300  millions,  what  per  cent 


446          WALSH'S  BUSINESS  ARITHMETIC 

of  the  actual  value  is  the  assessed  value?  (6)  What 
would  be  the  assessed  value  of  Mr.  Ritchie's  house, 
at  this  rate,  if  its  actual  value  is  $4000? 

2.  (a)  If  the  sum  to  be  raised  by  taxation  is  3  mil- 
lions, give  the  tax  rate  when  the  valuation  is  300 
millions.     What  would  be  (6)  Mr.  Ritchie's  valuation? 
(c)  His  tax  bill? 

3.  If  the  valuation  were  made  200  millions,  what 
would  be  (a)  the  tax  rate?     (b)  Mr.  Ritchie's  valu- 
ation?    (c)  His  taxes? 

4.  Why  would  there  be  no  difference  in  his  taxes 
when   there   was   a  change   in    the   valuation   of    his 
property? 

EQUALIZATION 

Whether  property  is  assessed  at  its  full  value  or  at 
any  per  cent  of  it,  the  tax  payment  on  any  parcel  is 
the  same.  All  that  an  owner  can  desire  is  that  all 
the  parcels  should  be  assessed  at  the  same  per  cent  of 
their  value.  If  he  feels  that  his  valuation  is  propor- 
tionately greater  than  that  of  his  neighbors,  he  can 
appeal  to  the  Board  of  Assessors. 

WRITTEN  EXERCISES 

1.  The  budget  requirements  for  city  purposes  are 
$2,973,468;    for  county  purposes,  $387,596;    and  for 
state  purposes  $294,810.     The  city  will  receive  from 
revenues  $843,495.     How  much  remains  to  be  derived 
from  taxation? 

2.  If  the  assessed  valuation  of  the  real  and  personal 
property  to  be  taxed  is  $275,483,500,  (a)  what  must 


FINANCING  BUSINESS 


447 


be  the  tax  on  each  $100  to  raise  the  amount  needed  as 
shown  in  the  preceding  example?  (Give  the  result 
correct  to  five  decimal  places.)  Find  the  tax  to  the 
nearest  cent  on  property  assessed  (6)  at  $2000,  (c) 
at  $30,000,  (d)  at  $400,000,  (e)  at  $5,000,000. 

3.  Find  H.  DeW.  Slater's  tax  at  $1.80  per  $100 
on  personal  property,  as  follows:  furniture,  $500;  clock, 
$10;   watch,  $25;   vehicle,  $100;   horse,  $175. 

4.  For  the  guidance  of  county  assessors,  the  State 
Board  of  Equalization  established  the  following  classi- 
fications and  valuation  of  an  acre  for  land  acreages  in 
Nevada  for  the  following  year: 


Cultivated 


1st  class 
3d 


50 


2d    class     $65 

4th       "        35 


Meadow 

1st   class   (1  ton  or  more  to  the  acre)  $30 
2d         "     (less  than  1  ton  to  the  acre)   18 

Pasture 

1st    class     $30  2d     class   $20 

3d  11  4th  7 

5.   The   classification    of    cultivated    land  is  deter- 
mined by  the  production  from  an  acre  as  follows: 


1st  class 

2d  class 

3d  class 

4th  class 

Alfalfa 
Hay 
Grain 

5    tons 
IK  tons 
1    ton 

3  to  5  tons 
under  1%  tons 
1400  to  2000  Ib. 

2  to  3  tons 
800  to   1400  Ib. 

under  2  tons 

under  800  Ib. 

448          WALSH'S  BUSINESS  ARITHMETIC 


(a)  Find  the  assessed  value  of  160  acres  of  land 
owned  by  Stephen  Luken,  40  acres  of  which  produced 
180  tons  of  alfalfa;  40  acres,  70  tons  of  hay;  40  acres, 
1200  bushels  of  wheat;  and  40  acres  of  first-class 
pasture.  (6)  Find  the  average  valuation  per  acre. 

6.  Neville  Hart  had  156  sheep  which  were  assessed 
at  $9  each;  68  hogs  at  $12;  42  pigs  at  $4;  35  cattle 
at  $38;  6  horses  at  $275;  and  3  mules  at  $195.  What 
was  the  total  valuation  of  the  foregoing? 

Find  the  amount  of  the  following  tax  bill: 

To  the  Treasurer  of  Fairfax  County,  Dr. 


Mt.  Vernon  District 


State  Taxes            35  £  on  $100 

1921 

County  Taxes.  .Levy,  30^;  Pensions,  5^;  County  Schools,  20& 
District  Schools,  15{;  Road  Tax,  25jf.    Total  95{  on  $100. 

SUBJECTS  OF  TAXATION 

State 
Taxes 

County 
Taxes 

Total 

STATE  CAPITATION  TAX 

Personal  Property  \  B  Val.  $3620 

;c  "      eoo 

(/) 
(j) 

07) 
(*) 

1 

CW 

(*•) 

(0 

50 

Total  Valuation                    $    (a) 
Dog  tax,  2  at  50^  each 
160  A.  val.  $40                          $6400 
40"      "      30                               (6) 
20"      "      25                               (c) 
20"     "      18                              (rf) 

Total  Valuation                             (e) 

Total 
Add 

tax 

5% 

(w) 
(n) 

(o) 

Received  payment  in  full 

.  (ody&lt&n,     Treasurer 


FINANCING  BUSINESS  449 

NOTE:  Enter  the  capitation  tax  and  the  dog  tax  only;  in  the  "Total" 
column.  Insert  at  (a)  the  total  value  of  the  personal  property,  at  (/)  the 
tax  at  35  £  at  (0)  the  tax  at  95  i,  and  at  (K)  the  sum  of  $)  and  (g).  Do  the 
same  with  the  tax  on  the  real  estate.  To  (ra)  add  5  %  of  itself  for  delay  in 
payment. 

UNITED   STATES  REVENUES 

WRITTEN  EXERCISES 

1.  During  the  year  preceding  the  war  the  receipts 
of  the   United   States   Government  from   all   sources 
were  $1,153,044,639.10.     The  total  disbursements  dur- 
ing the  same  period  were  $1,072,894,093.23.     Find  the 
balance. 

2.  Among  the  items  of  revenue  were: 

Customs  $213,185,845.63 

Internal  Revenue  (a) 

Ordinary  $303,486,474.94 

Emergency  84,278,302.13 

Income  tax 

Corporation  56,993,657.98 

Individual  67,943,594.63 

Sales  of  public  lands  1,887,661.80 

Consular  fees  1,466,572.72 

Profits  and  coinage  4,354,613.12 

Tax  on  bank  circulation  3,838.034.25 

Sale  of  two  battleships  12,535,275.96 

Patent  fees  2,329,510.36 

Forest  reserve  fund  2,883,783.73 

Receipts,  Dist.  of  Columbia  9,132,976.52 

Items  not  enumerated  (6) 


Insert  at  (a)  the  total  of  the  four  items  of  internal  revenue  receipts. 
Write  at  (c)  the  total  receipts  as  given  in  the  preceding  example.  Insert 
at  (6)  the  difference  between  (c)  and  the  sum  of  the  other  items,  adding 
the  latter  and  subtracting  then*  total  from  (c)  in  one  operation. 


450          WALSH'S  BUSINESS  ARITHMETIC 

DUTIES 

In  ordinary  times  about  one  fourth  of  the  total 
receipts  of  the  Government  are  obtained  from  duties. 
These  are  the  taxes  paid  on  imported  goods. 

The  rates  of  duty  are  fixed  by  the  tariff.  This  is 
an  act  of  Congress  specifying  the  duty  to  be  paid  on 
each  class  of  imports. 

THE  TARIFF 

On  some  articles  the  tariff  fixes  an  ad  valorem  duty. 
This  is  a  certain  per  cent  on  the  foreign  cost.  Bicycles 
and  motorcycles  pay  25%,  for  instance;  breech- 
loading  shot  guns  and  rifles,  35%;  silk  ribbons,  40%; 
pen  knives,  35  %. 

On  other  articles  there  is  a  specific  duty  of  so  much  a 
square  yard,  pound,  ton,  etc.  The  rate  on  window 
glass,  for  instance,  ranges  from  %j£  to  2fi  a  pound, 
according  to  its  size,  the  lowest  being  for  that  not 
exceeding  150  square  inches  in  surface.  On  sugar, 
the  rate  is  71/100f£  a  pound  with  higher  rates  for  the 
better  grades.  Grapes  are  charged  25  cents  a  cubic 
foot;  lemons  and  oranges  15  cents  a  package  not 
exceeding  1%  cu.  ft.,  25  cents  a  package  not  exceeding 
2%  cu.  ft.,  etc.,  and  %£  a  pound  in  packages  containing 
over  5  cu.  ft. 

DOUBLE  DUTIES 

A  few  articles  pay  both  a  specific  and  an  ad  valorem 
duty.  Perfumery  which  contains  alcohol  is  charged 
40^f  a  pound  and  60%;  that  without  alcohol  pays  only 
60%.  Lead  pencils  are  charged  36^  a  gross  and  25%; 
sweet  chocolate,  2^  a  pound  and  25  %. 


FINANCING  BUSINESS 


451 


THE  FREE  LIST 

Many  articles  are  admitted  free  of  duty;  among 
them  are  agricultural  implements,  blooded  cattle, 
bagging,  binding  twine,  books,  plants,  trees,  tea,  coffee, 
wool,  etc. 

A  DUTCH  INVOICE 

B.  E.  McAveney  &  Co.  import  two  cases  of  dry 
goods.  They  receive  the  following  invoice  from  the 
sellers  : 


ROTTERDAM,  Mar.  20,  1920 


Invoice  of  two  (2)  cases  of  dry  goods  marked 


Sold  to  Messrs.  A.  W.  Ross  &  Co.,  Omaha 

By  Bergen  &  Van  Brunt 
and  shipped  Mar.  23,  1920,  from  Amsterdam  per  S.S.  Victory. 


1609 
1610 


840  m  Dress  Goods  fl  1 . 80 

360  "  Laces  1.85 

180  "  Embroideries  2.10 

1200  "  Sateens  1.97% 

Less  5  % 


The  first  column  shows  the  mark  on  both  cases; 
the  second  gives  the  number  on  each.  No.  1609 
contains  three  kinds  of  goods,  and  No.  1610  one  kind. 
The  length  of  each  kind  is  given  in  meters  (ra)  and  the 
price  in  florins  (//) 

WRITTEN  EXERCISES 

1.  Copy  the  foregoing  invoice,  inserting  the  exten- 
sion for  each  item.  From  the  footing  deduct  5  %, 
and  insert  the  net  amount  due  in  florins. 


452 


WALSH'S  BUSINESS  ARITHMETIC 


2.  Find  the  equivalent  value  in  U.  S.  money  at  the 
gold  value  of  the  florin,  40.2  cents. 

3.  At  39.37  inches  to  the  meter  find  the  number  of 
yards  (a)  of  dress  goods.     (6)  Of  laces,     (c)  Of  embroi- 
deries,    (d)  Of  sateens. 

4.  (a)  Find  the  cost  of  each  of  the  four  items  in  the 
foregoing  invoice  after  the  deduction  of  the  discount 
of  5  %.     (b)  Express  the  net  cost  in  U.  S.  money  to  the 
nearest  dollar. 

PAYING  DUTIES 

The  goods  imported  by  B.  E.  McAveney  &  Co. 
were  landed  in  New  York  and  sent  in  bond  in  a  sealed 
car  to  Omaha.  Upon  their  arrival,  the  importers 
filed  at  the  custom  house  their  bill  of  lading  and  the 
foregoing  invoice  with  the  following  entry: 

OMAHA,  NEBR.,  Apr.  15,  1920 

Entry  of  Merchandise  imported  by  B.  E.  McAveney  &  Co. 
Invoice  dated  Rotterdam,  Mar.  20,  1920 
Arrived  at  New  York,  Mar.  31,  1920 


Marks 

Nos. 

Contents 

35% 

60% 

15% 

40% 

Total 

* 

I60«/,o 

Dress  Goods 
Laces 
Embroideries 
Sateens 

(«) 

(*) 

(c) 

(<0 

w 

(/) 

(*) 

(*) 

(0 

(;) 

)  35%  (*) 

j)  60%  (0 

(h)  15%  (m) 

(0  40%  (n) 

(o) 

6.   Copy  the  foregoing  entry.    Insert  (a  to  d),  the 
net  cost  of  the  various  items,  and  at  (e)  the  total. 


FINANCING  BUSINESS 


453 


Insert  (/  to  j)  the  value  in  TJ.  S.  money,  omitting  cents. 
Calculate  the  duty  on  each  item  (k  to  ri)  at  the  given 
rates.  Find  the  total  amount  (o). 

Two  copies  of  this  entry,  when  complete,  are  handed 
to  the  entry  clerk,  who  verifies  the  calculations,  affixes 
his  initials  at  (o),  and  passes  one  copy  along  to  the 
cashier.  He  also  designates  the  package  to  be  sent 
to  the  appraiser's  stores  with  the  invoice.  Here  the 
package  is  opened,  the  goods  measured,  their  char- 
acter determined,  and  the  rate  of  duty  noted  on  the 
invoice.  The  latter  is  returned  to  the  custom  house. 
If  the  figures  on  the  entry  are  correct,  a  liquidating 
clerk  certifies  thereto  by  affixing  his  initials  in  red. 
If  the  appraiser  changes  the  values  or  the  rates,  the 
liquidating  clerk  makes  out  a  new  duty  statement  in 
red  ink,  and  the  difference  to  be  collected  from  the 
importer  or  to  be  returned  to  him. 

6.   Find  the  duty  on  each  of  the  following: 


Classification 
of  goods 

Cost  at  place 
of  purchase 

U.  S.  coin  value 
of  foreign  money 

Rate  of 
duty 

a  Opera  glasses 
b  Watches 
c  Pickled  fish 
d  Vases 

1463.  90  francs 
£183  16s.  10  d. 
1237.  85  kroner 
2460.  50  lire 

19.3?f 
$4.8665 
26.8^ 
19.3{£ 

35% 
30% 

25% 
45% 

7.  What  is  the  duty  on  48,648  pounds  of  sugar 
testing  87°,  the  rate  being  71/100^  a  pound  for  sugar 
testing  75°,  and  26/lOOOc'  additional  for  each  degree 
above  75? 


CHAPTER  FIVE 


PROTECTING    THE    INDIVIDUAL 

A  fire  loss  of  $1000.  or  $100,000,  which  might  greatly 
embarrass  an  individual,  is  easily  shared  by  a  multitude. 
For  some  such  sum  as  $2.50  in  one  case  or  $250  in  the 
other,  an  insurance  company  will  provide  for  the  pay- 
ment of  the  loss  if  it  happens  during  the  year. 

FIRE  INSURANCE 

The  contract  is  evidenced  by  a  policy.  This  sets 
forth  that  the  specified  insurance  company  (the  under- 
writer)  in  consideration  of  a  certain  sum  (the  premium) 
agrees  to  insure  John  Doe  (the  insured)  for  a  specified 
term,  from  -  -  to  -  — ,  against  all  Direct  Loss  and 
Damage  by  Fire  and  by  removal  from  premises  en- 
dangered by  fire  to  an  amount  not  exceeding  - 
Dollars  to  the  following  property: 

INSURANCE  RATES 

The  rates  for  a  given  locality  are  generally  fixed  by 
a  Board  of  Underwriters,  who  take  into  consideration 
all  the  conditions.  The  following  shows  those  for 
$100  of  insurance  for  1  year  on  certain  types  of  houses 
in  a  given  section,  also  on  their  contents : 


Occupied  as 

Residence 

Apartment 

Store  and  Dwelling 

Construction 

Brick 

Frame 
16* 

Brick 
15* 

Frame 

Brick 

Frame 

Building 

10* 

20* 

20* 

40* 

Household  goods 

16 

20 

20 

24 

24 

40 

454 


FINANCING  BUSINESS  455 

FACTORS  DETERMINING  RATES 

A  rate  is  provided  for  every  type  of  building  and  for 
all  varieties  of  goods.  The  size  of  a  building,  the 
nature  of  the  roof,  the  water  supply  of  the  vicinity,  the 
character  of  the  business  carried  on,  the  proximity  to 
other  buildings  —  all  are  considered. 

An  extra  per  cent  is  sometimes  added  to  the  regular 
rates  when  the  water  supply  is  decreased;  a  per  cent 
is  deducted  when  the  insured  installs  fire-fighting 
equipment;  hose,  fire-extinguishers,  sprinklers,  etc. 

WRITTEN  EXERCISES 

1.  Find  the  premium  for  insuring  a  house  for  $7000 
and  household  goods  for  $5000  for  3  years  at  2%  times 
the  annual  rate  of  24  cents  for  the  former  and  32  cents 
for  the  latter. 

2.  A  manufacturer  paid   75   cents  insurance  on  a 
building  and  90  cents  on  stock,  the  former  being  insured 
for  $20,000  and  the  latter  for  $80,000.     a  What  was 
the  insurance  per  year?     He  installed  a  sprinkler  equip- 
ment at  a  cost  of  $6000.     If  his  insurance  was  reduced 
75%  thereby,   (6)  how  much  did  he  save  a  year  in 
excess  of  6  %  interest  on  the  cost  of  the  equipment  and 
6%  additional  allowed  for  its  depreciation? 

3.  A  dealer  in  dry  goods  occupied  the  7th,  8th,  and 
9th  floors  of  a  loft  building.     He  insured  goods  to  the 
amount  of  $48,000  on  the  7th  floor,  at  75 ff;     to  the 
amount  of  $45,000  on  the  8th  floor,  at  80^;     and  to 
the  amount  of  $65,000  on  the  9th  floor,  at  85^.     Find 
(a)  the  total  cost  of  the  insurance,     (b)  The  average 
rate  paid  on  the  total  amount  insured. 


456 


WALSH'S  BUSINESS  ARITHMETIC 


4.  A  merchant  insures  his  goods  while  in  a  ware- 
house for  25  days  at  19  %  of  the  yearly  rate  of  72  cents. 
What  is  the  premium  for  insurance  to  the  amount  of 
$25,000? 

250  X  .19  X  $.72 

Represent  the  number  of  $100  in  $25,000  as  250;  19%  as  .19;  and 
72  ff  as  the  decimal  of  a  dollar.  Write  the  answer. 

Rates  for  less  than  a  year  are  fixed  for  a  locality  by 
the  Board  of  Underwriters.  The  following  table  gives 
the  rates  for  one  section.  Insurance  generally  begins 
at  12  M  and  terminates  at  the  same  hour. 


SHORT-TERM  RATES 

Time 

% 

Time 

% 

Time 

% 

Time 

% 

Time 

% 

1  da. 

2 

8  da. 

9 

15  da. 

13 

1  mo. 

20 

6  mo. 

70 

2  " 

4 

9 

10 

16  " 

14 

45  da. 

27 

7  " 

75 

3  " 

5 

10 

10 

17  " 

15 

2  mo. 

30 

8  " 

80 

4  " 

6 

11 

11 

18  " 

16 

75  da. 

37 

9  " 

85 

5  " 

7 

12 

11 

19  " 

16 

3  mo. 

40 

10  ' 

90 

6  " 

8 

13 

12 

20  " 

17 

4  mo. 

50 

11  " 

95 

7  " 

9 

14 

13 

25  " 

19 

5  mo. 

60 

12  " 

100 

5.  A  person  who  has  taken  out  insurance  for  a  year 
from  March  3,  surrenders  his  policy  of  $10,000  on  the 
morning  of  April  17.  If  the  rate  was  54  cents  per  year, 
what  should  the  insurance  company  return? 

The  rate  for  45  days  (March  3  to  April  17)  being 
27  %  of  that  for  a  year,  the  company  would  refund  73  % 
of  100  times  54  cents.  If  the  policy  were  surrendered 
on  the  afternoon  of  April  17,  the  company  would  retain 
30%,  the  next  higher  rate,  returning  70%.  Periods 
other  than  those  specified  are  not  considered  by  in- 
surance companies  using  the  foregoing  short-term  rates. 


FINANCING  BUSINESS  457 

7.   An  insurance  company  canceled  policies  as  follows : 


Issued 

Face 

Term 

Rate 

Canceled 

a 

Jan. 

4. 

1921 

$16,000 

75 

da. 

55  1 

Feb. 

16, 

1921 

b 

Feb. 

5. 

1922 

20,000 

3 

mo. 

70ff 

Apr. 

10, 

1922 

c 

Mar. 

9, 

1921 

25,000 

25 

da. 

26? 

Mar. 

20, 

1921 

d 

Apr. 

(>, 

1922 

12,000 

1 

y. 

32^ 

Sep. 

30, 

1922 

e 

May 

8, 

1921 

15,000 

10 

mo. 

90  ji 

Jul. 

15, 

1921 

Find  (I)  the  premium  originally  paid  on  each; 
(II)  the  premium  retained  by  the  company;  (III)  the 
sum  returned  to  the  insured  upon  the  surrender  of  his 
policy. 

Since  the  great  majority  of  fires  cause  only  a  partial 
loss,  most  insurers  take  out  a  policy  for  a  sum  less  than 
the  value  of  the  property  insured.  A  man,  for  instance, 
may  insure  for  $5000  property  worth  $10,000.  If  the 
policy  contains  no  provision  to  the  contrary,  he  will  be 
reimbursed  in  full  for  any  loss  not  exceeding  $5000. 

CO-INSURANCE 

The  laws  of  many  states  require  that  a  provision 
similar  to  the  following  be  inserted  in  every  policy 
issued  in  these  states: 

"This  company  shall  not  be  liable  for  a  greater  pro- 
portion of  any  loss  or  damage  to  the  property  described 
herein  than  the  sum  hereby  insured  bears  to  eighty  per 
centum  (80%)  of  the  actual  cash  value  of  said  property 
at  the  time  such  loss  shall  happen.  ..." 

This  means  that  the  holder  of  policy  of  $5000  on 
property  worth  $10,000  will  receive  only  %  of  any  loss 
he  incurs  not  exceeding  the  face  of  the  policy.  To 
secure  payment  in  full  up  to  the  amount  of  his  insurance 
he  must  insure  for  $8000. 


SECTION  VII 

BUSINESS    MEASUREMENTS 

CHAPTER  ONE 
COMMON  TABLES 

A  housekeeper  buys  milk  by  the  quart;  a  dealer,  by 
the  100  pounds.  While  a  miller  pays  for  wheat  at  a 
given  price  a  bushel,  the  quantity  is  determined  by 
the  weight  of  the  grain. 

Small  dealers  now  sell  by  weight  such  vegetables  as 
potatoes,  onions,  tomatoes,  etc. 

In  some  states  the  use  of  dry  measures  in  selling 
goods  is  forbidden  by  law. 

The  following  tables  include  the  weights  and  meas- 
ures in  common  use. 

MEASURES  OF  LENGTH 

12  inches  (in.  or  ")  =  1  foot  (ft.  or  ') 
3  feet  =  1  yard  (yd.) 

5%  yards  =  1  rod  (rd.) 

320  rods  =  1  mile  (mi.) 

MEASURES  OF  SURFACE 

144  square  inches  (sq.  in.)  =  1  square  foot  (sq.  ft.) 

9  square  feet  =  1  square  yard  (sq.  yd.) 

30%  square  yards  =  1  square  rod  (sq.  rd.) 

160  square  rods  =  1  acre  (A.) 

640  acres  =  1  square  mile  (sq.  mi.) 

458 


BUSINESS  MEASUREMENTS  459 

MEASURES  OF  VOLUME 

1728  cubic  inches  (cu.  in.)  =  1  cubic  foot  (cu.  ft.) 
27  cubic  feet  =  1  cubic  yard  (cu.  yd) 

128  cubic  feet  =  1  cord 

AVOIRDUPOIS  WEIGHT 
16  ounces  (oz.)  =  1  pound  (Ib.) 
2000  pounds  =  1  ton  (T.) 

2240  pounds  =  1  long  ton 

DRY  MEASURE 

2  pints  (pt.)  =  1  quart  (qt.) 
8  quarts  =  1  peck  (pk.) 
4  pecks  =  1  bushel  (bu.) 

LIQUID  MEASURE 
2  pints  (pt.)  =  1  quart  (qt.) 
4  quarts         =  1  gallon  (gal.) 

SIGHT  EXERCISES 

1.  At  60  pounds  of  potatoes  to  the  bushel,  what 
should  be  the  weight  of  a  peck? 

2.  There  are  231  cubic  inches  in  a  gallon.     How 
many  cubic  inches  are  there  in  a  quart,  liquid  measure? 

3.  A    cubic    foot    of    water    weighs    1000    ounces. 
(a)  How  many  pounds  does  it  weigh?     (6)  Give  the 
weight  of  a  gallon  of  water,  assuming  that  there  are  7% 
gallons  to  the  cubic  foot. 

4.  A  section  of  land  is  a  square  mile.     How  many 
acres  are  there  in  a  quarter  section? 

5.  How  do  two  panes  of  glass  compare  in  area  when 
the  dimensions  of  one  are  6"  X  8"  and   those   of   the 
other  are  each  1%  times  as  great? 


460          WALSH'S  BUSINESS  ARITHMETIC 

6.  How  long  does  it  take  a  soldier  to  travel  2%  miles 
at  the  rate  of  3  miles  an  hour? 

7.  When  soldiers  march  88  yards  a  minute,  (a)  how 
many  minutes  do  they  take  to  march  a  mile  (1760  yd.)? 
(b)  How  many  miles  an  hour  do  they  march? 

8.  A  carrier  pigeon  flew  from  Rheims  to  Paris,  81 
miles,  in  4%  hours.     How  many  miles  an  hour  did  it 
fly? 

WRITTEN  EXERCISES 

1.  At  2150.42  cubic  inches  to  the  bushel   (a)  how 
many  cubic  feet  are  there  in  a  bushel?     (Give  answer 
to  two  decimal  places.)     (b)  How  much  does  this  differ 
from  the  approximate  rate  of  1.25  cubic  feet? 

2.  Find  the  difference  in  cubic  inches  between  IJi 
cubic  feet  and  2150.42  cubic  inches. 

3.  At  $4.8665  to  the  pound,  find  the  value  of  £247 
17s.  6d. 

4.  Express  4.835  miles  in  miles,  rods,  and  yards. 

5.  Find  the  average  height  of  forty  boys  four  of 
whom  measure  5  ft.  5  in.  each;   eight,  5  ft.  6  in.  each; 
twelve,  5  ft.  7  in.  each;  and  sixteen,  5  ft.  8  in.  each. 

6.  A  regiment  made  a  forced  march,  starting  at  8  A.M. 
It  rested  from  8:50  to  9,  from  9:45  to  10,  from  10:40 
to  11,  from  11:30  to  11:40,  from  12:10  to  1,  from  1:50 
to  2,  from  2:45  to  3,  from  3:40  to  4,  from  4:30  to  4:40, 
and  reached  its  journey's  end  at  5:10,  covering  a  dis- 
tance   of    19%    miles,     (a)  How  many   hours    elapsed 
between  the  start  and  finish?     (b)  How  much  time 
was  spent  in  rest?     (c)  Find  the  average  rate  of  travel 
an  hour  while  on  the  march. 


BUSINESS  MEASUREMENTS 


461 


1  barrack  bag 

lib. 

1  mosquito  bar 

14  oz. 

1  canvas  basin 

7  " 

1  bedding  roll 

11" 

12" 

1  blanket 

5  " 

2" 

1  canvas  bucket 

2" 

1  bedsack 

1  " 

U" 

1  mosquito  headnet 

14" 

1  lantern 

2" 

4" 

1  pack  carrier 

8" 

1  comb 

2" 

1  pkg.  paper 

15" 

1  cake  soap 

6" 

3  face  towels 

1" 

7.  Find  the  total  weight  of  the  following  items  of 
an  officer's  baggage  in  a  summer  campaign: 

1  pr.  woolen  breeches  1  Ib.  9  oz. 

2  "   cotton  drawers  1  "  11  " 
1  flannel  shirt  15  " 
1  pr.  marching  shoes  2  "  10  " 
5  "    stockings  10  " 

3  cotton  undershirts  1  "  8  *' 
1  clothing  roll  3  "  14  " 
3  handkerchiefs  2  " 
1  sweater  2  " 

1  poncho                                3  "  13  " 

1  housewife  4  " 

1  mirror  6  " 

1  shaving  outfit                     1  "  4  " 

1  toothbrush  and  dentrifice  4  " 

8.  When  a  soldier's  pace  is  30  inches,  (a)  how  many 
paces  does  he  take  in  going  a  mile?     (6)  When  he  goes 
3  miles  in  an  hour,  how  many  paces  does  he  take  in  a 
minute? 

9.  How  many  miles  does  a  horse  walk  in  an  hour 
(a)  when  it  walks  a  mile  in  16  minutes?     (6)  When  it 
takes  120  steps  of  33  inches  each  in  a  minute? 

METRIC  MEASURES  AND  WEIGHTS 

The  basis  of  the  metric  system  is  the  meter,  which 
is  one  forty -millionth  of  the  earth's  circumference  pass- 
ing through  the  poles. 

LONG  MEASURE 


10  millimeters  (' 
10  centimeters 
10  decimeters 
10  meters 
10  decameters 
10  hectometers 


1  centimeter  (cm) 
1  decimeter  (***) 
1  meter  (m) 
1  decameter  (dftm) 
1  hectometer  (*"*) 
1  kilometer  (km) 


462          WALSH'S  BUSINESS  ARITHMETIC 

The  subdivisions  of  each  metric  unit  are  denoted  by 
the  Latin  prefixes,  deci,  centi,  milli,  which  indicate 
tenths,  hundredths,  thousandths,  respectively. 
The  multiples  are  denoted  by  the  Greek  prefixes, 
deca,  hecto,  kilo  which  indicate  ten,  hundred, 
thousand,  respectively. 

The  denominations  in  common  use  are  the 
millimeter,  to  express  the  thickness  of  wire,  for 
instance;  the  centimeter,  to  express  the  width 
of  ribbon;  the  meter,  to  express  ordinary  lengths; 
and  the  kilometer  to  express  long  distances. 


WRITING  METRIC  NUMBERS 

To  express  84  centimeters,  write  either  84cm 
or  O.m84,  just  as  you  would  write  either  84  j£  or 
$0.84  to  express  84  cents.  To  indicate  3  meters, 
8  decimeters,  write  3m.80,  expressing  the  deci- 
meters as  centimeters;  just  as  you  would  use 
$3.80  to  express  3  dollars  8  dimes. 

SIGHT  EXERCISES 

1.  The  meter  is  39.37  inches.  Taking  40 
inches  as  its  length,  how  long  is  (a)  the  deci- 
meter? (6)  The  centimeter? 

The  accompanying  strip  is  1  decimeter  long,  divided  into  10  centimeters, 
the  first  of  which  is  subdivided  into  ten  millimeters,  the  others  showing  sub- 
division of  5  millimeters  each. 

2.  Give  the  approximate  number  of  centimeters  to 
the  inch. 

3.  About  what  size  collar  in  centimeters  should  be 


BUSINESS  MEASUREMENTS  463 

bought  in  Paris  by  an  American  soldier  who  wears  16- 
inch  collars? 

4.  About  what  is  the  bore  of  a  77  millimeter  gun? 

5.  Taking  the  kilometer  as  %  mile,  how  many  miles 
are  equal  to  (a)  40  kilometers,  (6)  200  kilometers? 

6.  When  the  bore  of  a  cannon  measures  155  milli- 
meters, what  is  it  approximately  in  inches? 

WRITTEN  EXERCISES 

1.  An  importer  bought  1879  meters  of  silk;    how 
many  yards  did  he  buy? 

2.  How  many  centimeters  is  it  in  width  if  it  is  27 
inches  wide? 

3.  Find  the  difference  between  a  kilometer  and  % 
mile  (a)  in  inches.     (6)  In  feet. 

4.  A  merchant  bought  7200  meters  of  silk  at  12  fr. 
50  a  meter  and  sold  it  at  $2.50  a  yard.     Find  his  profit. 

5.  How  far  does  a  cavalry  squad  travel  from  7 :45  A.M. 
to  11:15  A.M.  if  it  travels  2  hectometers  in  2  min. 
30  sec? 

DRY  AND  LIQUID  MEASURE 

The  unit  for  measuring  liquids,  grain,  etc.  in  small 
quantities  is  the  liter  (]).  Its  multiples  and  its  sub- 
divisions are  indicated  by  the  prefixes  used  with  the 
meter:  deci,  centi,  deca,  etc  The  liter  may  be  con- 
sidered as  a  hollow  cube  1  decimeter  long,  1  decimeter 
wide,  and  1  decimeter  high. 

Grain  in  large  quantities  is  sold  by  the  hectoliter. 

SIGHT  EXERCISES 

1.  There  are  231  cubic  inches  in  a  gallon,  (a)  How 
many  cubic  inches  are  there  in  a  quart?  (b)  How  many 


464          WALSH'S  BUSINESS  ARITHMETIC 

cubic  inches  are  there  in  a  cube  4  inches  long,  4  inches 
wide,  4  inches  high?  Taking  the  latter  as  the  equiva- 
lent of  a  liter,  how  many  more  cubic  inches  does  this 
contain  than  the  liquid  measure  quart? 

2.  A  liter  is  equivalent  to  .908  dry  quart,  (a)  How 
many  quarts  are  there  in  a  hectoliter?     (6)  About  how 
many  bushels? 

3.  About  how  many  gallons  are  there  in  a  hectoliter 
at  .9463  liquid  quarts  to  the  liter? 

METRIC  WEIGHTS 

The  unit  of  weight  is  the  gram,  used  in  one  or  the 
other  of  its  denominations  for  weighing  everything 
from  diamonds  to  iron  ore. 

The  prefixes  are  the  same  as  in  the  other  tables. 

A  kilogram  is  the  weight  of  a  liter  of  water. 

The  most  commonly  used  denomination  is  the  Idlo- 
gram  (generally  called  a  kilo).  This  is  equivalent  to 
2.2046  pounds.  The  metric  ton  of  1000  kilos  (the 
tonneau)  is  used  in  selling  articles  we  sell  by  the  ton. 
The  druggist  weighs  some  drugs  in  milligrams. 

SIGHT  EXERCISED 

Give  the  difference  between  the  long  ton  of  2240 
pounds  and  the  metric  ton  of  1000  kilos  of  2.2046 
pounds  each. 

WRITTEN  EXERCISE 

Find  the  weight  (a)  of  a  gallon  of  water  (231  cu.  in.) 
at  62.5  pounds  to  the  cubic  foot.  (6)  Of  a  quart  of 


BUSINESS  MEASUREMENTS  465 

water,     (c)  Of  a  liter  of  water,  taking  1.0567  quarts 
as  the  equivalent  of  a  liter. 


SQUARE  MEASURE 

PREPARATORY  EXERCISES 

1.  What  is  the  area  (a)  of  a  piece  of  land  12  meters 
long,  12  meters  wide?     (6)  Of  a  piece  of  leather  lm  2 
long,  lm  2  wide?     (c)  Of  a  piece  12dm  long,  12dm  wide? 

2.  (a)  How  many  square  decimeters  are  there  in  a 
square  meter?     (ft)  How  many  square  centimeters  are 
there  in  a  square  decimeter? 

100  square  centimeters  (emq)  =  1  square  decimeter  (dmq) 

100  square  decimeters  =  1  square  meter  (mq) 

100  square  meters  =  1  square  decameter  (dam<i) 

Observe  that  in  the  table  of  square  measure  there 
are  100  divisions  of  one  denomination  to  1  of  the  next 
higher. 

FARM  AREAS 

In  giving  the  area  of  a  field,  the  term  are  (a)  is  used, 
which  is  equivalent  to  100  square  meters.  The  are 
has  one  multiple,  the  hectare  (ha),  and  one  subdivision, 
the  centiare  (ca). 

WRITTEN  EXERCISES 

1.  What  is  the  duty  on  1000  tiles  measuring  75cm 
square  at  \%i  per  square  foot.     (1  sq.  meter  =  1.196 
sq.  yd.) 

2.  How  many  square  yards  are   there  in  a   roll  of 
cloth  48m  long  105cm  wide? 


466          WALSH'S  BUSINESS  ARITHMETIC 

3.  Find  the  number  of  pounds  in  a  barrel  of  oil  con- 
taining 45  gallons  when   I1  weighs     .8kg. 

4.  Find  the  number  of  square  yards  in  a  square 
meter. 

5.  How  many  square  meters  are  there  in  an  acre 
(4840  sq.  yd.)? 

6.  Find  the  number  of  acres  (a)  in  an  are.     (6)  In  a 
hectare. 

CUBIC  MEASURE 
Table 

1000  cubic  centimeters  (cmc)  =  1  cubic  decimeter  (dmc) 
1000  cubic  decimeters  =  1  cubic  meter  (mc) 

1000  cubic  meters  =  1  cubic  decameter  (damc) 

etc.  etc. 

Observe  in  the  table  of  cubic  measure  that  there  are 
1000  divisions  of  one  denomination  to  1  of  the  next 
higher. 

In  some  countries  the  abbreviation  for  cubic  meter  is 
(cbm).  In  others,  exponents  are  used  for  the.  square 
meter  (m*)  and  the  cubic  meter  (mS) . 

MEASURING  FIREWOOD 

Firewood  is  sold  by  the  stere  (8t),  which  is  a  cubic 
meter.  This  has  one  multiple,  the  decastere  (dast); 
and  one  subdivision,  the  dedstere  (dat). 

The  practice  of  selling  wood  by  weight  is  increasing.  The  buyer  of 
wood  by  the  stere  or  by  the  cord  cunnot  be  sure  of  the  amount  of  space 
occupied  by  the  "voids."  When  he  buys  by  weight,  he  requires  that  the 
wood  be  dry. 


BUSINESS  MEASUREMENTS  467 

WRITTEN  EXERCISES 

1.  Find  the  contents  in  cubic  meters  of  a  tank  3.m 
75  long,  2m  wide,  lm.50  deep. 

2.  How  many  liters  of  water  would  this  tank  con- 
tain? 

3.  What  would  be  the  weight  of  the  water  in  kilo- 
grams? 

4.  How  many    decaliters  of  grain  would  a  bin  of 
the  foregoing  dimensions  contain? 

5.  Find  the  weight  (a)  of  a  stere  of  white  pine  as- 
suming that  the  wood  occupies  only  75  %  of  the  space, 
and  that  the  weight  of  the  wood  is  38  %  of  the  weight 
of  the  same  volume  of  water.     (6)  Of  a  stere  of  white 
oak  with  the  same  per  cent  of  "voids,"  when  its  weight 
is  80  %  of  that  of  the  same  volume  of  water. 

6.  What  is  the  weight  of  a  cubic  foot  of  each  of  the 
foregoing  at  the  rate  of  1000  ounces  of  water  to  the 
cubic  foot? 


CHAPTER  TWO 
AREAS  AND   VOLUMES 

LINES  AND  ANGLES 

A   straight   line    (Fig.    1)   keeps  the  same  direction 
throughout  its  length.     A  broken  line  (Fig.  2)  is  made 


FIG.    1  FIG.    2  FIG.    3 

up  of  two  or  more  straight  lines.     A  curved  line  (Fig. 
3)  changes  its  direction  continually. 

When  two  straight  lines  meet  at  a  point,  they  are 
said  to  form  an  angle  (Fig.  4).  In  Fig.  5  are  shown 
two  angles  formed  by  two  lines.  These  are  called 
supplementary  angles.  When  these  supplementary 


FIG.   4  FIG.   5  l-'Ii!.    C 

angles  are  equal,  each  is  said  to  be  a  right  angle  (Fig.  6). 
The  angle  in  Fig.  5  that  is  smaller  than  a  right  angle  is 
called  an  acute  angle;  the  larger  one  is  called  an  obtuse 
angle.  The  term  oblique  angles  is  used  to  denote  those 
llmt  are  not  right  angles;  the  one  in  Fig.  4  and 
the  two  in  Fig.  5  are  oblique  angles. 

468 


BUSINESS  MEASUREMENTS  469 

The  size  of  an  angle  is  expressed  in  degrees  (and 
subdivisions).  The  lines  forming  the 
four  equal  angles  in  Fig.  7  at  the  center 
of  the  circle  divide  the  circumference 
into  four  equal  parts.  As  a  circle  con- 
tains 360°,  each  portion  contains  90°, 
and  eachangle  is  said  to  contain  90°.  FIG  7 


CIRCULAR  MEASURE 

60  seconds  (")  =  1  minute  (');   60  minutes  =  1  degree 
(°) ;  360  degrees  =  1  circle. 

ORAL  EXERCISES 

1.  How  many  degrees  are  there  in  the  angle  made 
by  the  hands  of  a  clock  (a)  at  3  o'clock?     (6)  At  9 
o'clock? 

2.  (a)  How  many  degrees  does    the   minute  hand 
move  in  going  from  XII  to  III?     (6)  How  many  degrees 
beyond  III  does  the  hour  hand  move  in  15  minutes? 
(c)  How  many  degrees  are  there  in  the  angle  made  by 
the  hands  of  a  clock  at  3:15?     (d)  How  many  degrees 
are  made  by  the  hands  of  a  watch  at  the  same  hour? 
(e)  By  the  hands  of  the  town-clock? 

DETERMINING  DIMENSIONS 

A  person  that  wishes  to  ascertain  an  area  must 
know  what  lines  to  measure  and  how  to  measure. 
Some  practice  can  be  had  about  the  class-room,  the 
school  building,  and  the  grounds.  A  yard  stick  or  a 
two-foot  rule  will  do  for  the  first,  a  steel  tapeline  for 


470 


WALSH'S  BUSINESS  ARITHMETIC 


the  others.     A  4-rod  chain  composed  of  100  links  is 
used  to  some  extent. 

Some  longer  distances  may  be  approximated  by 
pacing.  Each  pupil  should  determine  the  length  of 
his  ordinary  step:  (a)  by  measuring  a  single  one; 
and  (6),  by  measuring  the  distance  covered  by  20  or 
more,  and  finding  the  average,  doing  this  several  times 
and  comparing  results. 

AREA  OF  RECTANGLE 

A  rectangle  is  a  quadrilateral  (figure  of  four  sides) 
having  four  right  angles.  By  drawing  a  rectangle 

4  inches  by  3  inches  and  dividing  it 

into  1  inch  squares,  you  will  see  that 
there   are   3   rows   of   squares,    each 
containing  4  squares,  a  total  of  12 
squares.     Since  each  is  1  square  inch, 
the    rectangle    contains     12     square 
inches..    This  is  called  its  area. 
To  find  the  area  of  a  rectangle  in  square  units, 
multiply  its  length  in  the  linear  unit  by  its  width  in 
the  same  unit. 

This  may  be  stated  as  follows: 


FIG.   8 


Area  of  rectangle  =  Length  X  Width 


SIGHT  EXERCISES 

1.   Give  the  areas  of  rectangles  having  dimensions 
as  follows : 

a  25  ft.  by  96  ft.      6  88'  X  99'       c  64  yd.  X  12%  yd. 
d  44  rd.  by  25  rd.    e  98"  x  32"      /  66  ft.  x  16%  ft. 


BUSINESS  MEASUREMENTS  471 

2.  What  is  the  area,  in  square  feet,  of  a  rectangle 

(a)  12  feet  long,  9  inches  wide?     (b)   3  yards   long, 
18  inches  wide? 

Change  (a)  to  12  ft.  X  %  ft.       (b)  36  ft.  X  1%  ft. 

3.  Give  the  areas  in  square  feet. 

(a)  25  ft.  by  32  yd.     (6)  33  yd.  X  88  ft.     (c)  22  yd.  X  33%  ft. 

WRITTEN   EXERCISES 

1.    (a)  How  many  square  feet  will  1416  bricks  cover 
when  each  is  laid  on  its  side,  which  measures  4"  X  2K"? 

(b)  How  many  square  yards  will  1296  tiles  cover,  when 
each  is  7  inches  square? 


METHOD 
1416  X  1  X  5 

W         3  X  24        =  ?  (s 

1296  X  7  X  7 
(6)        36X36       "  ?  (sq'  yd'} 

In  (a)  change  4"  to  K  ft.  and  <%"  to  &  ft. 
In  (b)  change  1"  to  &  yd. 


2.  Find  the  area,  in  square  yards,  of  a  piece  of  carpet 
89  yards  long  27  inches  wide. 

3.  How  many  square  feet  will  be  covered  by  68 
boards  18  feet  long  8  inches  wide? 

4.  Find  the  number  of  acres  in  a  field  (a)  144  rods 
long,  32  rods  wide.     (b)   320  yards  long,   186  yards 
wide. 


472         WALSH'S  BUSINESS  ARITHMETIC 


METHOD 

144  X  32  320  X  186 


Since  there  is  no  linear  unit  corresponding  to  the 
acre,  indicate  the  area  of  (a)  in  square  rods  (144 
X  32)  and  the  division  of  this  product  by  160,  the 
number  of  square  rods  in  an  acre.  In  (6)  divide 
the  product  in  square  yards  by  4840,  the  number 
of  square  yards  in  an  acre.  Cancel  in  each  example. 


5.  A  field  is  924  yards  long  by  792  yards  wide. 
(a)  How  many  acres  does  it  contain?  (6)  How  many 
rods  of  barbed  wire,  4  wires  high,  will  be  needed  to 
inclose  it?  (c)  How  many  posts  6  feet  apart  will  be 
required?  (d)  If  boards  are  used,  how  many  would  it 
take  when  the  boards  are  12  ft.  long  and  the  fence 
is  3  boards  high? 

PARALLELOGRAMS 
A  quadrilateral  having  its  opposite  sides  and  oppo- 

. y      site  angles,  respectively  equal,  each 

\  \     to   each,   is   called    a     parallelogram 

\ \  (FiR.  9). 

The  area  of  any  parallelogram  is 
equal  to  that  of  a  rectangle  having 
the  same  length  and  width.  This  may  be  seen  in  Fig. 
10,  which  shows  a  right  triangle  A(x)D  out  from  the 
left  side  of  the  parallelogram  and  transferred  to  B(y)C 
at  the  right,  forming  the  rectangle  AByx.  The  area 


BUSINESS  MEASUREMENTS  47S 

of  the  latter  is  the  length  of  the  parallelogram   (AB) 

multiplied     by    its    width    (Ax). 

The  width  of  a  parallelogram  is 

generally  called  its  altitude,  and  is 

the  perpendicular  distance  between 

the  sides  constituting   its  length. 

Either  of  the  latter  sides  is  called 

the  base. 


Area  of  parallelogram  =  Length  X  Width 


This  is  generally  stated  as  the  product  of  the  base  by  the  altitude. 
NOTE:   The  line  that  measures  the  width  must  be  perpendicular  to  the 
length.     For  this  reason  it  is  sometimes  called  the  perpendicular. 

NAMES  OF  QUADRILATERALS 

While  a  rectangle  is  a  parallelogram,  a  parallelogram 
is  not  always  a  rectangle.  To  distinguish  between 
them,  a  rectangle  is  sometimes  called 
an  oblong,  while  the  term  rhomboid  is 
used  to  denote  a  parallelogram  con- 
taining oblique  angles.  An  equi- 
lateral rectangle  is  called  a  square; 
an  equilateral  rhomboid  is  called  a 
rhombus.  A  quadrilateral  that  has 
two  parallel  sides  is  called  a  tra- 
pezoid;  one  that  has  no  sides  paral- 
lel, a  trapezium. 

In  Fig.  11,  the  broken  line  half- 
way between  the  parallel  sides 
represents  the  "average  length" 
of  the  trapezoid,  and  the  broken  line  perpendicular  to 


474 


WALSH'S  BUSINESS  ARITHMETIC 


it  represents  the  width.    The  average  length  is  one- 
half  the  sum  of  the  lengths  of  the  two  parallel  sides. 


Area  of  trapezoid  =  l/2  (Sum  of  Parallel  sides  x  Per- 
pendicular) 


NOTE:   The  words  "perpendicular,"  "altitude,"  and  "width"  have  the 
.same  meaning  in  these  examples. 


DIMENSIONS  OF  A  PARALLELOGRAM 

If  a  person  desires  to  obtain  the  area  of  ABCD, 
•(Fig.  13)  which  has  opposite  sides  equal,  and  is,  there- 
fore, a  parallelogram,  he  may  measure 
any  convenient  side  as  a  base,  say 
DC.  In  this  case  he  will  measure  Bx 
as  the  perpendicular.  To  do  this,  he 
must  locate  x,  the  point  at  which 
a  perpendicular  from  B  will  intersect 
the  base  DC.  This  he  can  approxi- 
mate by  the  use  of  a  mounted  T-- 
square having  pins  F  and  G,  near  the 
extremities  of  one  arm, 
and  N  and  S  near  the  extremities  of  the 
other. 

Keeping  on  the  line  DC  at  each  end 
of  which  a  stake  is  placed,  he  locates 
the  point  x,  by  sighting  B  through  S  F 
and  N.  If  he  can  then  see  D  through 
G  and  F9  and  C  through  F  and  G,  the  hole  made  by 
the  staff  supporting  his  T-square  will  mark  the  point 
x. 


FIG.    13 


t 


s 

FIG.    14 


BUSINESS  MEASUREMENTS 


475 


THE  TRAPEZOID 

In  Fig.  15,  vw,  one  half  the  sum  of  AB  and  DC  (the 
parallel  sides),  is  multiplied  by  Ay  (the  length)  or 
Bx  to  find  the  area  of  the  trapezoid. 

Since  y  must  be  located  to  measure  Ay,   the  per- 
pendicular between  the  parallel  lines 
AB   and  DC,   it  will  be  unnecessary 
to  locate  v  and  w  in  field  work.     To 
check  the  result,  x  may    be  located 
and  Bx  measured.     If  these  two  lines 
are  parallel,  the  length  of  vw  may  be 
determined  by  taking  the  half  sum     D 
of  the  parallel  sides,  AB  and  DC. 

In  this  case  the  length  Ay  is  multiplied  by  the  aver- 
age width,  vw. 

TRIANGLES 

The  accompanying  figures  show  three  triangles, 
ABC,  DEF,  and  GIH,  with  broken  lines  drawn  parallel 


FIG.    15 


FIG.    18 


to  two  sides  of  each  triangle  to  form  a  parallelogram  that 
has  twice  the  area  of  its  corresponding  triangle. 


476          WALSH'S  BUSINESS  ARITHMETIC 

Taking  CB,  FE,  and  HI  as  the  respective  bases  of 
the  triangles,  their  altitudes  will  be  AB,  Dm,  and  Hn, 
respectively. 

Since  the  area  of  each  triangle  is  one-half  that  of 
the  corresponding  parallelogram,  the  area  of  a  triangle 
may  be  thus  expressed : 


Area  of  triangle  =  %  (Base  X  Altitude) 


The  triangle  ABC,  having  a  right  angle  at  B,  is 
called  a  right  triangle;  the  other  two  are  called  oblique- 
angled  triangles.  DEF,  having  three  angles  acute, 
is  called  an  acute-angled  triangle;  GIH,  containing 
an  obtuse  angle,  is  called  an  obtuse-angled  triangle. 

The  line  AC,  DF,  or  FD,  connecting  the  opposite 
angles  of  a  parallelogram  (Figs.  16-18),  is  called  its 
diagonal. 

POWERS  AND  ROOTS 

PREPARATORY  EXERCISES 

1.  Give  the  area  of  a  square  whose  base  measures 
a  5  in.      b  6  ft.      c  7  rd.      d  9  yd.      e  12  mi.     /  20  m- 

2.  Give  products : 

a  13  X  13    b  21  x  21    c  30  X  30    d  25  X  25    e  99  X  99 

To  indicate  that  a  number  is  to  be  multiplied  by 
itself,  write  above  it  to  the  right  a  small  2,  called  an 
exponent.  The  result  is  called  the  square  of  the 
number. 

3.  Give  squares  as  follows: 

a  132      b  212      c  302      d  322      e  402      /  412      g  802 


BUSINESS  MEASUREMENTS  477 

To  indicate  that  a  number  is  to  be  used  three  times 
as  a  factor,  use  3  as  an  exponent.  The  result  is  called 
the  cube  of  the  number. 

4.   Give  cubes  as  follows: 

a  23    6  33    c  43    d  53    e  63    /  73    g  83    h  93    i  103 

When  a  number  is  taken  4  times,  5  times,  etc.,  as 
a  factor,  the  result  is  called  the  4th  power,  5th  power, 
etc. 

SQUARE  ROOT 

6.    Give  the  base  of  a  square  whose  area  contains 
a  144  sq.  in.  b  100  sq.  ft.  c  81  sq.  yd. 

d  64  sq.  mi.  e  49  sq.  rd. 

The  answer  to  each  of  the  foregoing   requires   the 
finding  of  one  of  the  two  equal  factors  that  make  the 
given  number.     This  factor  is  called  the  square  root 
of  the  number.     The  sign  of  square  root  is  \/ 
6.    Give  square  roots  as  follows: 

a  V25     b  A/100     c  \/144     d  V400     e  V169    /  V^OO 

•y/  indicates  the  cube  root,  V  the  4th  root,  etc. 

WRITTEN    EXERCISES 

1.  What  is  the  side  of  a  square  plot  that  contains 
2304  square  feet? 

Draw  a  square.     Since  it  is  evident  that  the 
square  root  of  2304  is  between  40  and  50,  lay  off  a 


1600  sq.ft.' 


W 


portion  measuring  40  ft.  square, 


•K 


in  one  corner.    This  contains 


2304 


1600  sq.ft.     The  remainder  of  1600  (4  O2) 

the  plot  may  be  considered  to  OQ  , — yfnl 

comprise  two  rectangles  each  x  ttvtu 
ft.  wide,  one  of  them  being  40  ft. 
long  and  the  other  40  ft.  +  x  ft. 

long.    The  two  combined  form  a  single  rectangle 
FIG.  19                x  ft.  wide  and  80  ft.  +  x  ft.  long,  containing  704 


478          WALSH'S  BUSINESS  ARITHMETIC 

sq.  ft.  Since  704  contains  80  more  than  8  times,  try  8  as  the  value  of  x 
taking  88  ft.  for  the  length  of  the  combined  rectangles  and  8  ft.  for  the 
width.  The  product  of  88  and  8  being  704,  8  is  the  value  of  x  and  40  -f 
8,  or  48,  is  the  length  in  feet  of  a  side  of  the  square. 


METHOD 

Divide  2304  into  periods  of  two 
figures    each,    beginning    at    the     Ans.     4  8  (ft) 
right.    Write  16,  the  largest  square  23'04 

in   23,   under   the   latter,   and    4,  16 

its  square  root,  over  23.     Deduct       88       704 
16  from  23.     To  7,  the  remainder,  704 

annex  04.  To  the  right  of  704 
write  8,  twice  the  tens'  figure  of  the  root.  Taking 
this  as  a  trial  divisor,  divide  it  into  70  for  the  ones' 
figure.  Try  8,  writing  it  after  the  trial  divisor  and 
also  after  the  4  tens  of  the  root.  Multiply  88  by  8, 
writing  the  product  under  704.  Since  the  product 
agrees  with  the  latter,  8  is  correct,  and  the  root  is, 
therefore,  48.  Write  ft.  in  a  parenthesis.  Test 
by  multiplying  48  by  48. 


2.  Find  roots: 

a  A/8281      b  V5184      c 

3.  (a)  Multiply  7.  9  by  7. 9.  How  many  decimal  places 
are  there  in  the  product?     (b)  Find  the  square  of  .29. 
How  many  decimal  places  does  it  contain? 

4.  Extract  the  square  root  of  each  of  the  following: 

a  V5^29        b  V.0841        c  Vl3J59        d  \/34ltt 
6.   Extract  the  square  root  of  136,161. 


BUSINESS  MEASUREMENTS  479 


METHOD 

Proceed  as  in  the  previous  369  Ans. 

example.    Separate  136161  into  13'61'61 

periods    of    two    figures    each.  9 

Write  3  in  the  root  and  9  under     QQ 
13.     Subtract.    Bring  down  61. 
Take  twice  3  for  the  first  figure 


fi 

of  the  first  trial  divisor.     Di- 
vide  46  by  6  for  the  second 
figure  of  the  root.    Note,  however,  that  7  times  67 
would  be  greater  than  461,  and  try  6,  writing  it  in 
the  root  and  annexing  it  to  the  other  6.     Multiply 
66  by  6,  subtract.    Bring  down.    For  the  second  trial 
divisor,  take  twice  36,  the  portion  already  obtained, 
which  gives  72  as  the  first  two  figures.    Divide  65 
by  7  for  the  third  figure  of  the  root.     Write  9  in 
the  root  and  annex  9  to  72.     Multiply  729  by  9. 


6.   Find  the  root  of  each  of  the  following: 

a  V103041       b  V178929       c  V88804       d  \/443556 

THE  RIGHT  TRIANGLE 

PREPARATORY  EXERCISES 

NOTE:    In  making  graphs,  drawing  to  scale,  etc.,  the  use  of  cross-ruled 
paper  is  very  helpful  and  saves  much  time. 

1.   Draw  three  right  triangles  as  follows: 
a  On  a  scale  of  %"  to  1',  having  base  and  perpen- 
dicular of  3  ft.  and  4  ft.,  respectively. 

b  On  a  scale  of  }{"  to  1',  having  base  and  perpen- 
dicular of  5  ft.  and  12  ft.,  respectively. 


480          WALSH'S  BUSINESS  ARITHMETIC 

c  On  a  scale  of  %"  to  1',  having  base  and  perpendic- 
ular of  8  ft.  and  15  ft.,  respectively. 

2.  Measure  the  hypotenuse  of  each  triangle. 

The  results  will  show  that  the  hypotenuse  in   (a) 
will  be  5  ft.;  in  (6),  13  ft.;  and  in  (c),  17  ft. 

3.  Give  the  length  of  each  in  the  scale  drawing. 
Observe  the  following : 

32  =    9  52  =    25  82  =    64 

42  =  16  122  =  144  152  =  125 

52  =  25  132  =  169  172  =  189 

that  is,  the  square  of  the  hypotenuse  is  equal  to  the 
sum  of  the  squares  of  the  other  sides. 


Hypotenuse  2  =  Base2  -f-  Perpendicular 


APPLICATION  OF  SQUARE  ROOT 

1.  Find  the  length  of  the  missing  side  in  each  of  the 
following  triangles:   . 

a  Perpendicular,  45;  base,  24;  hypotenuse,  ? 
b  Perpendicular,  70;  base,  ?;  hypotenuse,  74 
c  Perpendicular,  ?;  base,  30;  hypotenuse,  78 
d  Perpendicular,  40;  base,  42;  hypotenuse,  ? 

2.  How  many  rods  of  fence  will  be  needed  to  enclose 
a  field  in  the  form  of  a  right  triangle  having  a  base 
of  48  rods  and  a  perpendicular  of  64  rods? 

3.  How  far  from  the  foot  of  a  building  is  the  foot 
of  a  ladder  50  feet  long  that  reaches  a  window  48 
feet  above  the  ground? 

4.  Find  the  diagonal  of  a  rectangular  field  (Fig.  16) 
165  yards  long,  144  yards  wide. 


BUSINESS  MEASUREMENTS  481 

AREAS  OF  OBLIQUE-ANGLED  TRIANGLES 

Owing  to  the  difficulty,  at  times,  of  measuring  the 
altitude  of  a  triangle,  it  becomes  necessary,  in  finding 
its  area,  to  use  the  lengths  of  its  sides. 

5.  Find  the  area  of  a  triangle  whose  sides  are, 
respectively,  21  rods,  24  rods,  and  27  rods. 


METHOD 


A/36  X  (36-21)  X  (36-24)  X  36-27 

24  / 

27  V  36  X  15  X  12  X  9  = 

A/58320  =  241.4953 


36  Ans.  241.5  (sq.  rd.) 

Take  the  square  root  of  the  continued  product  of 
the  half  sum  of  the  three  sides  (36)  by  the  difference 
between  this  half  sum  and  each  of  the  respective 
sides. 


6.  The  following  is  a  right  triangle.     Find  its  area 
by  the  foregoing  method.     Test  the  result  by  finding 
the  half  product  of  its  base  and  altitude.     The  sides 
are  63  ft.,  65  ft.,  and  16  ft. 

7.  The  following  is  an  isosceles  triangle;    that  is, 
one  having  two  equal  sides.     The  sides  are  29  yd., 
29  yd.,  40  yd.     Find  its  area. 

8.  In  an  isosceles  triangle,  the  unequal  side  is  called 
the  base.     A  perpendicular  let  fall  from  the  opposite 
angle  bisects  the  base.     Find  the  perpendicular  (alti- 
tude) of  the  triangle  in  the  last  example,  and  obtain 
its  area  by  the  use  of  the  base  and  the  altitude  as  the 
dimensions. 


482          WALSH'S  BUSINESS  ARITHMETIC 

9.  A  triangle  having  three  equal  sides  is  called  an 
equilateral  triangle,     (a)  Find  the  area  of  an  equilateral 
triangle  with  sides  of  100  yards.     (6)  Find  the  altitude. 

10.  Find  the  square  root  of  the  following: 

b  Vl.6  c  V.225 


NOTE:  In  finding  the  square  root  of  a  decimal  the  latter  must  have  an 
even  number  of  decimal  places.  Change  the  foregoing  to  (a)  \/-50;  (b) 
\/l  .60;  (c)  \/-2250.  In  pointing  off  a  mixed  decimal  whose  root  is  to  be 
found,  begin  at  the  decimal  point,  and  point  off  in  two  directions. 


AREAS  OF  POLYGONS 

A  polygon  of  three  sides  is  called  a  triangle;  of  four 
sides,  a  quadrilateral;  of  five  sides,  a  pentagon;  of 
six  sides  a  hexagon;  of  eight  sides,  an  octagon;  etc. 

In  the  case  of  a  regular  polygon,  the  sides  are  all 
equal,  as  well  as  the  angles. 

Give  the  name  of  a  regular  triangle.  Of  a  regular 
quadrilateral. 

A  regular  polygon  may  be  divided  by  lines  into  as  many  equal  triangles 
as  the  polygon  has  sides  each  triangle  having  its  apex  at  the  center.  Com- 
puters' tables  give  the  number  to  be  multiplied  by  the  square  of  the  length 
of  the  side  to  give  the  area.  This  number  is  .4330  for  the  equilateral  tri- 
angle; 1,  for  the  square,  2.5980,  for  the  regular  hexagon;  4.8284  for  the 
regular  octagon. 

To  find  the  area  of  an  irregular  polygon,  divide  it 
into  triangles,  two  less  than  the  number  of  sides. 

WRITTEN  EXERCISES 

1.  Find  the  area  (a)  of  an  equilateral  triangle  having 
sides  of  17  feet,  (b)  Of  a  regular  octagon  having  6- 
inch  sides,  (c)  Of  a  regular  hexagon  having  sides  of 
11  inches. 


BUSINESS  MEASUREMENTS  483 

2.  ABCD  is  a  trapezium.     To  find  its  area,  the  line 
AC  has  been  measured  and  found  to  be  42  rods  long. 
The  perpendiculars  Bx  and  Dy  meas- 
ure,   respectively,  24   rods   and    32 

rods.  Find  the  area  of  the  trapezium, 
which  is  in  square  rods,  %  of  (42  X 
32)  +  K  of  (42  X  24).  Shorten  the 
work  by  multiplying  Y2  of  (24  +  32) 
by  42.  " 

3.  Find  the  sum  of  the  areas  of  the  two  triangles 
in  the  foregoing  trapezium  by  determining  the  area 
of  each  triangle  from  the  following: 

In  ABC:  AB  34  rods,  BC  20  rods,  AC  42  rods 
"  ADC:  AD  40  rods,  DC  26  rods,  AC  42  rods 
Compare  the  two  results. 

4.  A  room  is  18  feet  wide,  24  feet  long,  and  9  feet 
high,     (a)  How  many  square  yards  are  there  in  the  ceil- 
ing?    (b)  How  many  square  feet  are  there  in  the  floor? 
(c)  Find  the  number  of  square  yards  in  one  side  wall 
(18'  X  9r) .     (d)  In  the  opposite  wall  after  the  deduction 
of  the  space  occupied  by  a  door  (6'  9"  X  4').     (e)  Find 
the  number  of  square  yards  in  an  end  wall,  deducting 
for  two  windows,  each  6'  X  3'.     (/)  In  the  opposite 
wall,  deducting  for  a  door   of  the  size  given   above. 
(g)  Find  the  number  of  running  feet  of  baseboard  in 
the  room,  deducting  the  space  occupied  by  the  doors. 
(It)  Find  the  number  of  square  feet,  when  the  base- 
board is  9"  high. 

5.  Determine,  by  making  the  necessary  measure- 
ments, (a)  the  number  of  square  yards  of  plastering 
required  for  your  classroom,     (b)  The  number  of  cubic 


484          WALSH'S  BUSINESS  ARITHMETIC 

feet  of  air  space,  (c)  The  number  of  square  feet  of 
floor  space,  (d)  The  area  of  the  exposed  window  glass. 
6.  A  box  of  window  glass  contains  50  square  feet 
as  nearly  as  possible.  Find  the  number  of  panes  in  a 
box  for  each  of  the  following  sizes: 

a    6"x  8"     6     8"xlO"     c     8"xl2"     d     9"xl2"     e    9"xl6" 
/  10"xl5"     g  10"xl6"     h  12"xl2"     i    12"xl5"    j  12"xl8" 

BOARD  MEASURE 

Lumber  is  sold  by  the  board  foot.  A  board  foot  is 
1  foot  wide,  1  foot  long,  and  1  inch  thick.  When 
the  thickness  is  less  than  an  inch,  it  is  taken  as  1  inch. 
A  board  12  ft.  long,  1  foot  wide,  and  1  inch  thick 
contains  12  board  feet;  if  of  the  same  length  and 
thickness  and  8  inches  wide,  it  contains  8  board  feet; 
16  feet  long,  6  inches  wide,  and  1  inch  thick,  8  board 
feet;  etc. 


Board  feet  =  Feet  long  X  feet  wide  X  inches  thick 


SIGHT  EXERCISES 

1.  Give  the  number  of  board  feet  in  planks,  scant- 
lings, etc.,  having  dimensions  as  follows: 

Length  Width  Thickness  Length  W'idth  Thickness 

a      12'          %'  r  b      16'         %'  2" 

c       18'         %'  2"  d      12'         %'  I" 

DEALERS'  TABLES 

In  a  dealer's  tables,  the  number  of  board  feet  in  a 
board,  scantling,  plank,  joist  is  given,  for  various 
lengths  in  feet  and  widths  and  thicknesses  in  inches. 


BUSINESS  MEASUREMENTS 


485 


Length 
in  ft. 

Width  and  thickness  in  inches 

•xi 

2X6 

2x9 

2^X6 

2^X8 

3X3 

3x6 

4x7 

4x10 

8 
10 
12 
14 
16 
18 

2% 

8 

12 

10 

1SK 

6 

12 

18% 

26ft 

2.  From  the  foregoing  dimensions  give  the  number 
of  board  feet  (a)  by  lines.  (6)  By  columns. 

WRITTEN  EXERCISES 

1.  Find  the  number  of  board  feet  in  each  of  the 
following : 

a  2  sills,  4"  X  4"  X  10'  62  plates,  2"  X  4"  X  10' 

c  2      "    4"  X  4"  x  14'  d  2       "      2"  X  4"  X  14' 

e  16  pieces,  2"  X  4"  X  12'  for  studs,  rafters,  roosts. 

2.  Draw  to  a  convenient  scale  the  end  view  of  a 
shed  13  feet  high  in  front,  8  feet  high  in  the  back,  and 
12  feet  deep.     Find  (a)  the  area  of  the  end.     (6)  The 
length  of  the  edge  of  the  roof,  if  it  projects  6  inches 
beyond  the  front  and  the  back  of  the  shed,     (c)  Find 
the  area  of  the  roof  if  the  length  of  the  shed  is  18  feet 
and  the  roof  projects  6  inches  beyond  each  side  also. 

SHINGLES 

Shingles  vary  in  width.  A  bundle  of  250  shingles 
contains  a  total  width  of  250  times  4  inches,  or  1000 
inches.  When  shingles  are  laid  to  form  a  roof,  each 
row  so  overlaps  the  under  one  as  to  leave  only  a 


486          WALSH'S  BUSINESS  ARITHMETIC 

portion  of  the  length  of  the  latter  exposed  to  the 
weather,  generally  4  inches.  Since  a  shingle  is  con- 
sidered as  4  inches  wide,  the  space  covered  by  each 
is  4"  X  4". 

3.  (a)  How  many  shingles  with  4"  X  4"  exposed,  will 
cover  a  square  foot?     (6)  How  many  bundles  of  250 
shingles  will  be  required  for  a  roof  14'  X  19'?     (c)  Find 
the  cost  of  the  shingles  at  $30  a  1000  (4  bundles  of 
250  each).     A  whole  bundle  must  be  bought  for  any 
excess. 

4.  How  many  gallons  of  paint  will  be  required  to 
paint  the  sides  and  the  back  of  the  shed  in  Ex.  2  at 
the  rate  of  a  gallon  to  45  square  yards  for  the  first 
coat,  to  50  square  yards  for  the  second  coat,  and  to  55 
square  yards  for  the  third  coat?     (Give  results  to  the 
nearest  K  gallon). 

5.  How  many  hours  of  work  will  a  painter  require 
for  three  coats,  if  he  takes  an  8  hour  day  for  each  100 
square  yards  in  the  first  coat  and  for  each  80  square 
yards  in  the  second  and  third  coats?     (Give  result 
to  nearest  %  day.) 

THE  CIRCLE 

The  circle  is  a  plane  surface  bounded  by  a  curved 
line  called  the  circumference.  Every 
point  on  the  latter  is  equi-distant 
from  a  point  (C)  called  the  cento-. 
The  line  mn  passing  through  the 
center  of  a  circle  and  beginning  and 
terminating  in  its  circumference,  is 
called  a  diameter.  Each  of  the  semi- 
diameters  Co,  Cm,  and  Cn,  is  called  a  radius.  A  portion 


BUSINESS  MEASUREMENTS  487 

of  the  circumference,  om  or  on,  is  called  an  arc.  A 
portion,  oCm,  or  oCn,  of  the  area  of  a  circle,  bounded 
by  an  arc  and  two  radii  is  called  a  sector. 

The  circumference  of  a  circle  whose  diameter  is 
1  inch  has  been  found  to  be  3.1416  inches.  This 
ratio  of  the  circumference  to  the  diameter  is  expressed 
by  the  Greek  letter  w  (pronounced  pi) . 


Circumference  =  TT  x  Diameter 


You  can  find  this  ratio  approximately  by  measuring  the  circumference 
of  a  cylindrical  tumbler  with  a  tape  line  and  comparing  this  length  with  that 
of  the  diameter  of  the  tumbler. 

DIAMETER  AND  CIRCUMFERENCE 

NOTE:  In  the  following  exercises    take   3%  as   the 

value  of  TT. 

SIGHT  EXERCISES 

1.  Give  the  diameter  of  the  trunk  of  a  tree  when  its 
circumference  is  22  inches. 

22  in.  -h  3# 

2.  A  bicycle  wheel  has  a  diameter  of  28   inches. 
How  far  will  the  bicycle  travel  during  one  revolution 
of  the  wheel? 

3.  Give  the  circumference  of  a  circle  whose  diameter 
is  1%  inches. 

4.  How  long  will  be  the  circumference  of  a  circle 
drawn  by  a  compass  when  the  points  are  %  inch  apart? 

5.  What  is  the  circumference  of  the  bottom  of  a 
tent  when  its  diameter  is  7  feet? 

6.  Give  the  circumference  described  by  the  minute 
hand  of  a  clock  if  the  hand  is  8  feet  long. 


488 


WALSH'S  BUSINESS  ARITHMETIC 


WRITTEN   EXERCISES 

1.  How  many  revolutions  are  made  by  a  bicycle 
wheel  in  going  a  mile  (5280  ft.)  when  the  radius  of  the 
wheel  is  28  inches? 

2.  What  is  the  diameter  of  a  circle  whose  circum- 
ference is  1  mile? 

3.  A  circular  running  track  is  16%  feet  wide,  and 
its  interior  circumference  is  l/2  mile.     Find  the  length 
of  the  circumference  of  the  outer  side  of  the  track. 

4.  Find  the  difference  between  the  length  of  the 
circumference  of  a  circular  pond  375  yards  in  diameter 
when  TT  is  taken  as  3%  and  when  it  is  taken  as  3.1416. 

AREA  OF  CIRCLE 

WTien  a  circle  (Fig.  22)  is  divided  into  a  large  num- 
ber of  equal  parts,  and  these  are  arranged  as  is  shown 


//  R 


FIG.    22 


no. 


.in  Fig.  23,  they  form  a  parallelogram  whose  altitude 
is  Rj  the  radius  of  the  circle,  and  whose  base  measures 
TT  R,  its  semi-circumference.  The  area  is,  therefore, 


Area  of  Circle  =  *  x  Square  of  Radius 


BUSINESS  MEASUREMENTS 


489 


WRITTEN  EXERCISES 

1.  Taking  3%  as  the  value  of  TT,  find  the  areas  of 
circles,  as  follows: 

a  Diameter,  14  ft.     6  Radius,  21  in.     c  Diameter,  35  yd. 

2.  (a)  Find  the  area  in  square  yards  inclosed  by  a 
circular    running    track    having    a    circumference    of 
%  mile.     (6)  Find  the  area  inclosed  by  the  outer  circum- 
ference of  the  track,  when  the  width  of  the  track  is 
16K  feet,     (c)  Find  the  area  of  the  track,  which  is  the 
difference  between  (a)  and  (b). 

RECTANGULAR  SOLIDS 

A  solid  having  six  faces,  the  opposite  ones  of  which 
are  equal  and  parallel,  is  called 
a  parallelopipedon.  When  the 
faces  are  rectangles,  it  is  called 
a  right  parallelopipedon. 
When  the  faces  are  equal,  it  is 
called  a  cube. 

The  term  solid  is  applied  to 
bodies  that  are  hollow.  The 
volume  of  a  solid  may  mean 
the  quantity  it  will  hold. 


FIG.    24. 


VOLUMES 

The  number  of  cubic  units  in  the  volume  of  a  rec- 
tangular solid  is  equal  to  the  combined  product  of  its 
three  linear  units  of  the  corresponding  kind. 


Volume  of  Rectangular  Solid 
Length  x  Breadth  x  Height 


490          WALSH'S  BUSINESS  ARITHMETIC 

SIGHT  EXERCISES 

1.  Give  the  number  of  cubic  units  in  the  volume 
of  each  of  the  following  rectangular  solids,  their  dimen- 
sions in  linear  units  being 

a  1%  X  17  X  8       b  12  X  19  X  33%       c  16  X  41  X  25 
d  66%  X  11  X  6       e  12  X  37  X  16%      /  12  X  31  x  75 

2.  How  many  cubic  inches  will  a  canteloupe  crate 
hold,  when  its  dimensions  are  12"  X  12"  X  22"?     An 
orange   crate   measures    12"  X  12"  X  24";    how   many 
cubic  feet  does  it  contain? 

WRITTEN   EXERCISES 

1.  Find  the  number  of  gallons  that  can  be  contained 
in  a  tank  17  ft.  6  in.  long,  12  ft.  3  in.  wide,  and  4  ft. 
7  in.  deep. 

Express  each  dimension   in  inches. 

-j^.     .j        ,       .   ~0.,       .  •       \     .1 

Divide  by  231   (cu.  in.)  the  contents 


^  ^Av  w 

X    IT!«     X 


of  a  gallon. 

2.  Give  the  capacity,  in  bushels,  of  a  bin  measuring 
24'  X  16'  X  14'.  Take  2150.4  cubic  inches  to  the 
bushel. 


24  X  12  X  16  X  12  X  14  X  12         .  Muvltip^  eadl 

sion  by  12  to  express  it 

2150'4  in  inches. 

3.  How  many  cubic  feet  are  there  in  a  bale  of  cotton 
whose  dimensions  are  54"  X  27"  X  45".     Give  answer 
to  nearest  cubic  foot. 

4.  How  long  a  piece  of  bagging,  54  inches  wide, 
will  be  required  (a)  to  wrap  the  four  sides  of  the  bale? 
(b)   To  cover  the  two  ends?     (c)  How  much  bagging 


BUSINESS  MEASUREMENTS 


491 


will  be  saved  by  compressing  the  bale  to  one  measuring 
54"  x  27"  x  22}£"? 

5.  At  55  pounds  to  the  cubic  foot,  how  many  pounds 
of  anthracite  coal  are  there  in  a  bin  6  ft.  8  in.  wide, 
10  ft.  6  in.  long,  when  the  depth  of  the  coal  is  4  ft.  6  in.? 

THE  PRISM 

A  solid  having  two  equal  and  parallel  faces  and  the 
remaining  faces  parallelograms  is  called 
a  prism.  One  of  these  parallel  faces  is 
called  the  base  of  the  prism.  When 
the  other  faces  are  rectangles,  the  prism 
is  said  to  be  a  right  prism.  A  prism  is 

designated  as  triangu- 

lar, quadrilateral,  hexa- 

gonal, according  to  the 

number  of  sides  in  the  base. 

THE   CYLINDER 

The  cylinder  has  two  parallel  circular 
bases    and    a   curved    lateral    surface. 
The  lateral   surface  of  a  prism  or  a 
cylinder,  that  is,  the  surface  exclusive 
of  that  of  the  bases,  is  also  called  its  convex  surface. 

LATERAL  SURFACE  OF  PRISM  OR  CYLINDER 
PREPARATORY  EXERCISES 

A  factory  is  making  a  number  of  hollow  prisms  and 
cylinders  20  inches  high.  For  the  lateral  surface  of 
each  a  strip  of  sheet  iron  is  taken,  20  inches  wide. 


FIG- 


FIG.    26 


492          WALSH'S  BUSINESS  ARITHMETIC 

1.  Give  the  length  of  the   strip  required  for  the 
lateral  surface  of  each  of  the  following  regular  prisms 
when  the  length  of  each  side  of  the  base  is  7  inches, 
making  no  allowance  for  overlapping: 

a  Triangular          b  Square          c  Hexagonal 

2.  What  is  the  area  of  the  strip  in  each  case? 

3.  How  long  must  be  the  strip  for  a  cylinder  14 
inches  in  diameter? 


Lateral  Surface  of  Prism  (Cylinder)  = 
Perimeter  (Circumference)  of  Base  x  Height 


WRITTEN  EXERCISES 

1.  How  many  square  yards  of  painting  are  required 
to  give  three  coats  to  the  outside  of  a  cylindrical  silo 
28  feet  in  diameter  and  36  feet  high? 

2.  Find  the  convex  surface  of  a  marble  octagonal 
shaft  6  ft.  8  in.  high,  when  each  side  of  the  base  meas- 
ures 4  inches. 


VOLUME  OF  PRISM;  OF  CYLINDER 
Volume  of  Prism  (Cylinder)  =  Area  of  Base  x  Height 


WRITTEN   EXERCISES 

1.  Find  the  volume  in  cubic  feet  of  a  silo  28  feet  in 
diameter  and  35  feet  high. 

2.  At  231  cubic  inches  to  the  gallon,  find  the  capacity 
of  a  standpipe  42  feet  high  and  14  feet  in  diameter. 


BUSINESS  MEASUREMENTS 


493 


PYRAMID  AND   CONE 
Surface 

The  lateral  faces  of  a  right  pyramid  are  isosceles 
triangles,  the  base  of  each 
being  a  side  of  the  base  of 
the  pyramid,  and  the  ver- 
tices of  the  triangles  meet- 
ing at  a  common  point  called 
the  apex.  Pyramids  are 
triangular,  square,  etc.  The 
area  of  ABC  is  one-half  the 
product  of  AB  by  BC. 

To  make  a  hollow  paper 
cone  take  a  sector,  HlyJ 
(Fig.  28),  bring  together 
the  radii  HI  and  H J,  which , 
makes  the  arc  lyJ  the  circumference  of  the  base  of 
the  cone  (Fig.  29).  The  area  of  the  sector  is  one-half 


FIG.    27 


FIG.    28 


FIG.    29 


the  product  of  the  arc  lyJ  by  the  radius  HI.  In 
Fig.  27  the  line  Ax  represents  the  slant  height  of  the 
pyramid;  in  the  cone,  Fig.  29,  any  straight  line 


494          WALSH'S  BUSINESS  ARITHMETIC 

drawn  from  the  vertex  to  the  circumference  of  the 
base  is  its  slant  height. 

SIGHT  EXERCISES 

1.  Give  the  area  of  a  lateral  face  of  a  square  pyramid 
when  a  side  of  its  base  measures  24  inches  and  its  slant 
height  99  inches. 

NOTE:  Remember  that  the  slant  height  of  the  pyramid  is  the  altitude    of 
a  triangular  face. 

2.  When  the  base  is  a  square  50  feet  on  a  side,  and 
the  slant  height  is  47%  feet,  give  the  surface  of  the 
four  lateral  faces. 

3.  WTiat  is  the  lateral  surface  of  a  cone,  the  circum- 
ference of  the  base  being  49  feet  and  its  slant  height 
50  feet? 


Lateral  Surface  of  Regular  Pyramid  (Cone)  =  %  Per- 
imeter (Circumference)  of  Base  x  Slant  Height 


WRITTEN   EXERCISES 

1.  Find  the  lateral  surface  of  a  triangular  pyramid, 
having  a  slant  height  of  37  yards  and  each  side  of  the 
base  23  yards. 

2.  Find   the   entire   surface   of   a   square   pyramid 
(including  the  base)  when  its  slant  height  is  16^  feet, 
and  each  side  of  the  base  is  7  feet  3  inches. 

3.  Find  the  lateral  surface  of  a  cone  having  a  base 
14  feet  in  diameter  and  a  slant  height  of  22  feet. 

4.  Draw  a  rectangle  3"  X  1%".     On   two   adjacent 
sides  construct  isosceles  triangles  having  sides  of  3%". 
Measure  the  altitude  of  each  triangle. 


BUSINESS  MEASUREMENTS  495 

Take  these  sides  as  the  scale  drawing  of  two  of  the 
lateral  faces  of  a  rectangular  pyramid  having  a  base 
24  inches  by  14  inches,  with  edges  measuring  25  inches 
each.  Calculate  the  slant  height  of  each  of  these 
faces. 

(a)  Find  the  lateral  surface  of  the  pyramid,  (b)  Its 
entire  surface. 

Volume  of  Pyramid.     Of  Cone 

By  making  a  hollow  pyramid  of  any  height  (alti- 
tude), and  a  prism  having  the  same  base  and  altitude, 
respectively,  as  the  pyramid,  it  will  be  found  that  the 
prism  will  contain  the  contents  of  the  pyramid  three 
times. 


Volume  of  Pyramid  (Cone)  =  %  (Area  of  Base  x  Altitude) 


WRITTEN  EXERCISES 

1.  Find  the  volume  (a)  of  a  square  pyramid,  each 
side  of  the  base  measuring  23  inches  and  the  altitude 
45  inches,     (b)  Of  a  rectangular  pyramid  of  the  same 
height  when  the  sides  of  the  base  are  12  inches  and 
14  inches,  respectively. 

2.  Find  the  volume  of  a  cone  15  feet  high,  with  a 
base  7  feet  in  diameter. 

3.  How  many  bushels  of  wheat  are  there  in  a  freight 
car  40  feet  long  and  8%  feet  high  when  the  depth  of  the 
grain  is  5%  feet? 

4.  How  many  square  yards  of  canvas  are  required 
for  a  conical  tent  14  feet  in  diameter  at  the  base  and 
having  a  slant  height  of  12  feet? 


496          WALSH'S  BUSINESS  ARITHMETIC 

5.  (a)  How  many  square  feet  of  boards  will  be  re- 
quired to  inclose  a  rectangular  plot  174  yards  long 
and  126  yards  wide  with  a  rectangular  fence  6  feet 
high?     (6)  How  many  boards  12  feet  long  8  inches 
wide  will  be  needed?     (c)  How  many  board  feet,  if 
the  boards  are  1  inch  thick? 

6.  (a)  How  many  square  feet  are  there  in  the  fore- 
going plot?     (6)  A  walk  4  feet  wide  is  made  inside  the 
fence;    what  is  the  area  of  the  plot  inside  the  walk? 

(c)  How  many  square  feet  does    the    walk    contain? 

(d)  How  many  square  feet  are  there  in  a  4-foot  walk 
along  the  fence  on  the  outside? 

7.  (a)  How  many  square  yards  are  there  in  the  space 
covered  by  a  wall  3  feet  wide  inclosing  a  cellar  24  feet 
wide  and  48  feet  long?     (6)  How  many  cubic  yards  of 
material  are  there  in  the  wall,  if  the  latter  is  9  feet 
high?     (c)  What  is  the  outside  perimeter  of  the  wall? 
(d)  The  inner  perimeter?     (e)  The  average  of  the  two? 

8.  How  many  cubic  feet  of  material  are  there  in  a 
sewer  pipe  4  feet  long  whose  inner  diameter  is  13  inches 
and  the  outer  diameter  15  inches? 

9.  In  framing  a  diploma  that  measures  18"  X  12", 
a  girl  uses  a  cardboard  "mat"  that  covers  one  inch  of 
each  side  of  the  diploma  and  shows  3  inches.     One 
inch  of  each  side  of  the  mat  is  covered  by  the  frame, 
which  is  2  inches  wide.     Find  (a)  the  outer  dimensions 
of  the  framed  picture;    (b)  the  dimensions  of  the  mat; 
(c)  the  area  of  the  opening;    and  (d)  the  number  of 
running  feet  of  frame  needed,  making  allowance  for 
the  waste  at  the  corners. 


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SEP 


.  21  1.*. 
SEP  4  1920 
NOV  2  1920 

0261 81  AO 
NOV  18 1920 

APft    18  1921 
JUN  30  1921 


FEB  28 


1846; 


/#%$•. 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


